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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

Evaluate and simplify the following derivatives. d dx -(x In²x)
Find dy/dx for the following functions. y (x² - 1) sin x sin x + 1
Find dy/dx for the following functions.y = cos2 x
Evaluate the derivatives of the following functions.ƒ(x) = tan-1 (e4x)
Evaluate and simplify the following derivatives. d dx (xe-10)
Find the derivative of the following functions by first expanding the expression. Simplify your answers.g(r) = (5r3 + 3r + 1)(r2 + 3)
Evaluate the derivatives of the following functions.ƒ(x) = sec-1 (ln x)
Evaluate and simplify the following derivatives. d -(2x sin x√3x - 1) = dx
Find dy/dx for the following functions.y = sin x cos x
Use implicit differentiation to find dy/dx. √x + y² = sin y 2
Find dy/dx for the following functions. y || 1 sin x 1 + sin x
Evaluate and simplify the following derivatives. 1/3 -,-)¹/³ d V 1/1 (13 dv 3v² + 2v + 1.
Use implicit differentiation to find dy/dx. √x² + y² 2 || 5x + 2y³ 3
Find dy/dx for the following functions. y COS X sin x + 1
Evaluate and simplify the following derivatives. d ӨР (tan (sin 9))
Evaluate and simplify the following derivatives. 31²-1 d/3² dt\3² + 1 -3
Evaluate the derivatives of the following functions.ƒ(w) = sin (sec-1 2w)
Find the derivative of the following functions.s(t) = 4√t - 1/4 t4 + t + 1
Evaluate the derivatives of the following functions.ƒ(y) = cot-1 (1/(y2 + 1))
Evaluate and simplify the following derivatives. d (4u² + u du 8u+ 1/
Find the derivative of the following functions.g(w) = 2w3 + 3w2 + 10w
Evaluate and simplify the following derivatives. d dx -(csc³ 3x)
Use implicit differentiation to find dy/dx. X3 x+y x - y
Evaluate the derivatives of the following functions.ƒ(t) = ln (tan-1 t)
Find dy/dx for the following functions.y = e6x sin x
Evaluate and simplify the following derivatives. d do (4 tan (0² + 30 + 2))
Find the derivative of the following functions.f(t) = 6√t - 4t3 + 9
Use implicit differentiation to find dy/dx.6x3 + 7y3 = 13xy
Find dy/dx for the following functions.y = x sin x
Find the derivative of the following functions.f(x) = 10x4 - 32x + e2
Use implicit differentiation to find dy/dx.(xy + 1)3 = x - y2 + 8
Use implicit differentiation to find dy/dx. y x+1 y У-1
Evaluate the derivatives of the following functions.ƒ(t) = (cos-1 t)2
Find dy/dx for the following functions.y = sin x + 4e0.5x
Find the derivative of the following functions.g(x) = 6x5 - x
Evaluate the derivatives of the following functions.ƒ(x) = cos-1 (1/x)
Find dy/dx for the following functions.y = e-x sin x
Evaluate the derivatives of the following functions.ƒ(x) = sec-1 √x
Find dy/dx for the following functions.y = 5x2 + cos x
Find the derivative of the following functions by first expanding the expression.h(x) = (x2 + 1)2
Evaluate and simplify the following derivatives. d dw -(e-w In w)
Find dy/dx for the following functions. x sin x 1 + cos x
Evaluate and simplify the following derivatives. d dx -(log3 (x + 8))
Evaluate and simplify the following derivatives. d dx (2x²-x)
Evaluate and simplify the following derivatives. d dx sin
Evaluate and simplify the following derivatives. dx (xups-x)- P
a. Find an equation of the line tangent to the given curve at a.b. Use a graphing utility to graph the curve and the tangent line on the same set of axes. y = x + 5 x-1 a = 3
Find the derivative of the following functions by first expanding the expression. Simplify your answers.h(x) = √x (√x - 1)
Evaluate the derivatives of the following functions.ƒ(x) = sin (tan-1 (ln x))
Evaluate the derivatives of the following functions.ƒ(s) = cot-1 (es)
Evaluate the derivatives of the following functions.ƒ(x) = 1/tan-1 (x2 + 4)
Find d2y/dx2.x + y2 = 1
Evaluate and simplify the following derivatives. d - (x sec=¹ x)/x = - 2 dx √3
a. Find an equation of the line tangent to the given curve at a.b. Use a graphing utility to graph the curve and the tangent line on the same set of axes. y = 2x² 3x - a = 1
Find an equation of the line tangent to the graph of f at the given point.ƒ(x) = tan-1 2x; (1/2, π/4)
Find d2y/dx2.2x2 + y2 = 4
a. Find an equation of the line tangent to the given curve at a.b. Use a graphing utility to graph the curve and the tangent line on the same set of axes. y = 312 X a = 1
Find d2y/dx2.x + y = sin y
Evaluate and simplify the following derivatives.ƒ'(1) when ƒ(x) = x1/x
Evaluate and simplify the following derivatives. d (tan=¹ e^^)| dx lx=0
Find an equation of the line tangent to the graph of f at the given point.ƒ(x) = cos-1 x2; (1/12, p/3)
Find d2y/dx2.x4 + y4 = 64
Evaluate and simplify the following derivatives.ƒ(1) when ƒ(x) = tan-1 (4x2)
a. Find an equation of the tangent line at x = a.b. Use a graphing utility to graph the curve and the tangent line on the same set of axes. = y= et 4 x; a = 0
Find d2y/dx2.e2y + x = y
a. Find an equation of the tangent line at x = a.b. Use a graphing utility to graph the curve and the tangent line on the same set of axes.y = -3x2 + 2; a = 1
Find d2y/dx2.sin x + x2y = 10
a. Find an equation of the tangent line at x = a.b. Use a graphing utility to graph the curve and the tangent line on the same set of axes.y = x3 - 4x2 + 2x - 1; a = 2
Find dy/dx.y = x5/4
a. Find an equation of the tangent line at x = a.b. Use a graphing utility to graph the curve and the tangent line on the same set of axes.y = ex; a = ln 3
Find dy/dx.y = (5x + 1)2/3
Let f(x) = x2 - 6x + 5.a. Find the values of x for which the slope of the curve y = f(x) is 0.b. Find the values of x for which the slope of the curve y = f(x) is 2.
Use the Chain Rule to find the derivative of the following functions.y = (2x6 - 3x3 + 3)25
Let f (t) = t3 - 27t + 5.a. Find the values of t for which the slope of the curve y = f(t) is 0.b. Find the values of t for which the slope of the curve y = f(t) is 21.
Calculate the derivative of the following functions.y = log8 |tan x|
Find ƒ'(x), ƒ''(x), and ƒ''(x). f(x) = X x + 2
Compute the derivative of the following functions. y 2e + 3e-* 3
Determine the slope of the following curves at the given point.xy + x3/2y-1/2 = 2; (1, 1)
Find dy / dx. y = У 2x 4x 3
Find an equation of the line tangent to the following curves at the given point.y = 3x3 + sin x; x = 0
Find y" for the following functions.y = x sin x
Let ƒ(x) = 2x3 - 3x2 - 12x + 4.a. Find all points on the graph of f at which the tangent line is horizontal.b. Find all points on the graph of f at which the tangent line has slope 60.
a. Find all points on the graph of f at which the tangent line is horizontal.b. Find all points on the graph of f at which the tangent line has slope 12.Let ƒ(x) = 2ex - 6x.
Find an equation of the line tangent to the following curves at the given point. y 4x x² + 3 x = 3
Find dy / dx . y = √(1 + x¹/³)²
Calculate the derivative of the following functions. VI + cot²x
Find dy / dx. X || y √√x + x
Find dy / dx.y = x(x + 1)1/3
Find y" for the following functions. y = 1/1e²c 2 ex cos x
Determine the slope of the following curves at the given point. √x + √y¹ = 2; (1, 1)
Find y" for the following functions.y = cos x
Calculate the derivative of the following functions. √(3x-4)² + 3x
Find y" for the following functions.y = ex sin x
Compute the derivative of the following functions.ƒ(x) = xe7x
Compute the derivative of the following functions.g (t) = 2tet/2
Find ƒ'(x), ƒ"(x), and f(3)(x) for the following functions.f(x) = 10ex
Find ƒ'(x), ƒ'(x), and ƒ(3)(x) for the following functions.f(x) = 3x3 + 5x2 + 6x
Evaluate the derivative of the following functions at the given point.y = t - t2; t = 2
Find ƒ'(x), ƒ"(x), and f(3)(x) for the following functions. f(x) = x²7x8 x + 1
Compute the derivative of the following functions.f(x) = 15e3x

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