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study help
mathematics
precalculus
Thomas Calculus Early Transcendentals 13th Edition Joel R Hass, Christopher E Heil, Maurice D Weir - Solutions
Use differentials to approximate the value of the expression. Compare your answer with that of a calculator.(2.02)4
a. Find ƒ -1(x).b. Graph ƒ and ƒ -1 together.c. Evaluate dƒ/dx at x = a and dƒ -1/dx at x = ƒ(a) to show that at these points dƒ-1/dx = 1/(dƒ/dx).ƒ(x) = 2x + 3, a = -1
Use implicit differentiation to find dy/dx.x2y + xy2 = 6
a. Find ƒ-1(x).b. Graph ƒ and ƒ-1 together.c. Evaluate dƒ/dx at x = a and dƒ-1/dx at x = ƒ(a) to show that at these points dƒ-1/dx = 1/(dƒ/dx).ƒ(x) = 5 - 4x, a = 1/2
Given y = ƒ(u) and u = g(x), find dy/dx = ƒ′(g(x))g′(x).y = 6u - 9, u = (1/2)x4
Use implicit differentiation to find dy/dx.x3 + y3 = 18xy
Given y = ƒ(u) and u = g(x), find dy/dx = ƒ′(g(x))g′(x).y = 2u3, u = 8x - 1
a. Find ƒ-1(x).b. Graph ƒ and ƒ-1 together.c. Evaluate dƒ/dx at x = a and dƒ -1/dx at x = ƒ(a) to show that at these points dƒ-1/dx = 1/(dƒ/dx).ƒ(x) = (1/5)x + 7, a = -1
Use implicit differentiation to find dy/dx.2xy + y2 = x + y
Use implicit differentiation to find dy/dx. y2 || x x + 1 1
Given y = ƒ(u) and u = g(x), find dy/dx = ƒ′(g(x))g′(x).y = sin u, u = 3x + 1
Use implicit differentiation to find dy/dx.x3 - xy + y3 = 1
Given y = ƒ(u) and u = g(x), find dy/dx = ƒ′(g(x))g′(x).y = cos u, u = e-x
a. Find ƒ -1(x).b. Graph ƒ and ƒ -1 together.c. Evaluate dƒ/dx at x = a and dƒ -1/dx at x = ƒ(a) to show that at these points dƒ -1/dx = 1/(dƒ/dx).ƒ(x) = 2x2, x ≥ 0, a = 5
Use implicit differentiation to find dy/dx. x³ || 2x - y x + 3y
a. Show that ƒ(x) = x3 and g(x) = 3√x are inverses of one another.b. Graph ƒ and g over an x-interval large enough to show the graphs intersecting at (1, 1) and (-1, -1). Be sure the picture shows the required symmetry about the line y = x.c. Find the slopes of the tangents to the graphs of ƒ
Use implicit differentiation to find dy/dx.x2(x - y)2 = x2 - y2
Given y = ƒ(u) and u = g(x), find dy/dx = ƒ′(g(x))g′(x).y = √u, u = sin x
a. Show that h(x) = x3/4 and k(x) = (4x)1/3 are inverses of one another.b. Graph h and k over an x-interval large enough to show the graphs intersecting at (2, 2) and (-2, -2). Be sure the picture shows the required symmetry about the line y = x.c. Find the slopes of the tangents to the graphs at h
Use implicit differentiation to find dy/dx.(3xy + 7)2 = 6y
Given y = ƒ(u) and u = g(x), find dy/dx = ƒ′(g(x))g′(x).y = sin u, u = x - cos x
Let ƒ(x) = x3 - 3x2 - 1, x ≥ 2. Find the value of dƒ-1/dx at the point x = -1 = ƒ(3).
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x. y = У 1 -7
Given y = ƒ(u) and u = g(x), find dy/dx = ƒ′(g(x))g′(x).y = tan u, u = πx2
Find the derivative of y with respect to x, t, or θ, as appropriate. y 1 In 3x
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x. y = (-1) √x 2 -10
Let ƒ(x) = x2 - 4x - 5, x > 2. Find the value of dƒ -1/dx at the point x = 0 = ƒ(5).
Given y = ƒ(u) and u = g(x), find dy/dx = ƒ′(g(x))g′(x).y = -sec u, u = 1/x + 7x
Use implicit differentiation to find dy/dx.x = sec y
Suppose that the differentiable function y = ƒ(x) has an inverse and that the graph of ƒ passes through the point (2, 4) and has a slope of 1/3 there. Find the value of dƒ-1/dx at x = 4.
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x. y = X 8 + x - x 4
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x.y = (2x + 1)5
Use implicit differentiation to find dy/dx. y sin = 1 - xy ||
Use implicit differentiation to find dy/dx.xy = cot (xy)
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x. y = √3x² - 4x + 6
Suppose that the differentiable function y = g(x) has an inverse and that the graph of g passes through the origin with slope 2. Find the slope of the graph of g-1 at the origin.
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x.y = (4 - 3x)9
Find the derivative of y with respect to x, t, or θ, as appropriate. y = ln 3 X
Use implicit differentiation to find dy/dx.x + tan (xy) = 0
Find the derivative of y with respect to x, t, or θ, as appropriate.y = ln 3x + x
Use implicit differentiation to find dy/dx.x4 + sin y = x3y2
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x. y = cot ㅠ X
Find the derivative of y with respect to x, t, or θ, as appropriate.y = ln (t2)
Find dr/dθ. 7/80 € + €/20/² = 0^2 - r
Use implicit differentiation to find dy/dx.x cos (2x + 3y) = y sin x
Find the derivative of y with respect to x, t, or θ, as appropriate.y = ln (t3/2) + √t
Use implicit differentiation to find dy/dx.e2x = sin (x + 3y)
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x.y = sec (tan x)
Use implicit differentiation to find dy/dx.ex2y = 2x + 2y
Find the derivative of y with respect to x, t, or θ, as appropriate.y = ln (sin x)
Find the derivative of y with respect to x, t, or θ, as appropriate.y = ln (θ + 1) - eθ
Find dr/dθ.θ1/2 + r1/2 = 1
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x.y = tan3 x
Find the derivative of y with respect to x, t, or θ, as appropriate.y = (cos θ) ln (2θ + 2)
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x.y = 5cos-4 x
Find the derivative of y with respect to x, t, or θ, as appropriate. y x4 4 In x x4 16
Find the derivative of y with respect to x, t, or θ, as appropriate.y = ln x3
Find dr/dθ.sin (r θ) = 1/2
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x.y = e-5x
Find the derivative of y with respect to x, t, or θ, as appropriate.y = (ln x)3
Find dr/dθ.cos r + cot θ = er θ
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x.y = e2x/3
Find the derivative of y with respect to x, t, or θ, as appropriate.y = t (ln t)2
Use implicit differentiation to find dy/dx and then d2y/dx2.x2 + y2 = 1
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x.y = e5-7x
Find the derivative of y with respect to x, t, or θ, as appropriate.y = t ln √t
Use implicit differentiation to find dy/dx and then d2y/dx2.x2/3 + y2/3 = 1
Write the function in the form y = ƒ(u) and u = g(x). Then find dy/dx as a function of x.y = e(4√x+x2)
Find the derivatives of the function. P= V3-t
Find the derivatives of the function. 9 = √³/2r - p² 2
Find the derivative of y with respect to x, t, or θ, as appropriate. y In t t
Find the derivative of y with respect to x, t, or θ, as appropriate. y t Vln t
Find the derivatives of the function. S 4 З п -sin 3t + 4 5 п -cos 5t
Use implicit differentiation to find dy/dx and then d2y/dx2.y2 = ex2 + 2x
Find the derivative of y with respect to x, t, or θ, as appropriate.y = (x2 ln x)4
Use implicit differentiation to find dy/dx and then d2y/dx2.y2 - 2x = 1 - 2y
Find the derivatives of the function. S = sin 3πt 2 + cos 3πt 2
Find the derivative of y with respect to x, t, or θ, as appropriate. y = ln x 1 + ln x
Use implicit differentiation to find dy/dx and then d2y/dx2.2√y = x - y
Find the derivative of y with respect to x, t, or θ, as appropriate. y = x ln x 1 + ln x
Use implicit differentiation to find dy/dx and then d2y/dx2.xy + y2 = 1
If x3 + y3 = 16, find the value of d2y/dx2 at the point (2, 2).
Find the derivatives of the function. = sinx-cos³x y 5x X
Find the derivatives of the function.r = (csc θ + cot θ)-1
If xy + y2 = 1, find the value of d2y/dx2 at the point (0, -1).
Find the derivatives of the function. y = (5 2x) 3 + 1 8 x +1 4
Find the derivatives of the function.r = 6(sec θ - tan θ)3/2
Find the derivatives of the function. y = 18 -(4-2²3) (3x − 2)6 +
Find the derivative of y with respect to x, t, or θ, as appropriate. y = ln 1 x√x + 1
Find the derivative of y with respect to x, t, or θ, as appropriate.y = ln (ln x)
Find the slope of the curve at the given points.y2 + x2 = y4 - 2x at (-2, 1) and (-2, -1)
Find the derivatives of the function.y = x2 sin4 x + x cos-2 x
Find the derivative of y with respect to x, t, or θ, as appropriate.y = ln (ln (ln x))
Find the slope of the curve at the given points.(x2 + y2)2 = (x - y)2 at (1, 0) and (1, -1)
Find the derivative of y with respect to x, t, or θ, as appropriate. y || 1 + Int 1 - Int
Find the derivative of y with respect to x, t, or θ, as appropriate. y || 1 + x In 2 1 - x X
Find the derivative of y with respect to x, t, or θ, as appropriate.y = θ(sin (ln θ) + cos (ln θ))
Verify that the given point is on the curve and find the lines that are (a) Tangent (b) Normal to the curve at the given point.x2 + xy - y2 = 1, (2, 3)
Find the derivative of y with respect to x, t, or θ, as appropriate. y = Vln Vt
Find the derivative of y with respect to x, t, or θ, as appropriate.y = ln (sec θ + tan θ)
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