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mathematics
calculus 6th edition

Questions and Answers of Calculus 6th edition

Differentiate the function.y = log2(e–x cos πx)
Find y´ and y´´.y = ln x/x2
Find y´ and y´´.y = ln(sec x + tan x)
If f(x) = In x/x2, find f´(1).
If f(x) = ln(1 + e2x), find f´(0).
Find d9/dx9(x8 In x).
Find an equation of the tangent line to the curve at the given point.y = ln(x3 – 7), (2,0)
Find an equation of the tangent line to the curve at the given point.y = ln(xex2), (1, 1)
(a) Find y' by implicit differentiation. (b) Solve the equation explicitly for y and differentiate to get y' in terms of x. (c) Check that your solutions to parts (a) and (b) are consistent by
Find dy/dx by implicit differentiation.2√x + √y = 3
Find dy/dx by implicit differentiation.2x3 + x2y – xy3 = 2
Find dy/dx by implicit differentiation.x4(x + y) = y2(3x – y)
Find dy/dx by implicit differentiation.y5 + x2y3 = 1 + yex2
Find dy/dx by implicit differentiation.x2y2 + x sin y = 4
Find dy/dx by implicit differentiation. √√√x + y = 1 + x²y²
Find dy/dx by implicit differentiation.1 + x = sin(xy2)
Find dy/dx by implicit differentiation.y sin(x2) = x sin(y2)
Find dy/dx by implicit differentiation.√xy = 1 +x2y
Find dy/dx by implicit differentiation.tan(x – y) = y/1 + x2
Find dy/dx by implicit differentiation.ey cos x = 1 + sin(xy)
Find dy/dx by implicit differentiation.sin x + cos y = sin x cos y
If f(x) + x2[f(x)]3 = 10 and f(1) = 2, find f´(1).
If g(x) + x sin g(x) = x2, find g´(0).
Find y" by implicit differentiation.√x + √y = 1
Find y" by implicit differentiation.x4 + y4 = a4
Find the derivative of the function. Simplify where possible.g(x) = √x2 – 1 sec–1 x
Find the derivative of the function. Simplify where possible. F(θ) arcsin √sin θ
Differentiate the function.y = 5ex + 3
Use a graph to find a number δ such that if 5 < x < 5 + δ then x2/√x – 5 > 100
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f'(r) exists, then limx→r f(x) = f(r).
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.d2y/dx2 = (dy/dx)2
(a) If f(t) = t2 – √t, find f'(t). (b) Check to see that your answer to part (a) is reasonable by comparing the graphs of f and f'.
The unemployment rate U(t) varies with time. The table (from the Bureau of Labor Statistics) gives the percentage of unemployed in the US labor force from 1993 to 2002.(a) What is the meaning of
Use a graph to find a number δ such that if |x – 1| 2x 2 x² + 4 - 0.4 < 0.1
Find an equation of the tangent line to the given curve at the specified point.y = 2x/x + 1, (1, 1)
The table shows the estimated percentage P of the population of Europe that use cell phones. (Midyear estimates are given.)(a) Find the average rate of cell phone growth (i) From 2000 to 2002 (ii)
A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 5.f(t) = t–1 – t
The number N of locations of a popular coffeehouse chain is given in the table. (The numbers of locations as of June 30 are given.)(a) Find the average rate of growth(i) From 2000 to 2002 (ii) From
Use the definition of a derivative to find f'(x) and f"(x). Then graph f. f', and f" on a common screen and check to see if your answers are reasonable. f(x) = 1 + 4x – x2
Use the definition of a derivative to find f'(x) and f"(x). Then graph f. f', and f" on a common screen and check to see if your answers are reasonable.f(x) = 1/x
Differentiate.f(x) = √x sin x
Differentiate the function. f(x) = 186.5
Differentiate.f(x) = sin x + 1/2 cot x
Differentiate.g(x) = √x ex
Differentiate the function.f(x) = √30
Differentiate.y = 2 csc x + 5cos x
Differentiate it.y = ex/x2
Differentiate.g(t) = t3 cos t
Differentiate.y = ex/1 + x
Differentiate the function.F(x) = 3/4x8
Differentiate.g(t) = 4 sec t + tan t
Differentiate.g(x) = 3x – 1/2x + 1
Differentiate.h(θ) = csc θ + eθ cot θ
Differentiate.f(t) = 2t/4 + t2
Differentiate.Y(u) = (u–2 + u–3)(u5 – 2u2)
Differentiate the function.h(x) = (x – 2)(2x + 3)
Find the derivative of the function.f(x) = (1 + x4)2/3
Differentiate.y = 1 + sin x/x + cos x
Differentiate.F(y) = (1/y2 – 3/y4)(y + 5y3)
Differentiate the function.y = x–2/5
Find the derivative of the function.g(t) = 1/(t4 + 1)3
Differentiate.f(θ) = sec θ/1 + sec θ
Differentiate.R(t) = (t + et)(3 – √t)
Find the derivative of the function.f(t) = 3√1 + tan t
Differentiate.y = 1 – sec x/tan x
Differentiate.y = x3/1 – x2
Differentiate the function.V(r) = 4/3πr3
Find the derivative of the function.y = cos(a3 + x3)
Differentiate.y = sin x/x2
Differentiate.y = x + 1/x3 + x – 2
Differentiate the function.R(t) = 5t–3/5
Find the derivative of the function.y = a3 + cos3x
Differentiate.y = csc θ (θ + cot θ)
Differentiate.y = t2 + 2/t4 – 3t2 + 1
Differentiate the function.A(s) = –12/s5
Find the derivative of the function.y = xe–kx
Differentiate.f(x) = xex csc x
Differentiate.y = t/(t – 1)2
Differentiate the function.B(y) = cy–6
Find the derivative of the function.y = 3 cot(nθ)
Differentiate.y = x2 sin x tan x
Differentiate.y = (r2 – 2r)er
Differentiate the function.G(x) = √x – 2ex
Find the derivative of the function.g(x) = (1 + 4x)5(3 + x – x2)8
Differentiate.y = 1/s + kes
Find the derivative of the function.h(t) = (t4 – 1)3 (t3 + 1)4
Differentiate.y = v3 – 2v√v/v
Differentiate the function.F(x) = (1/2x)5
Find the derivative of the function.y = (2x – 5)4(8x2 – 5)–3
Differentiate.z = w3/2(w + cew)
Find the derivative of the function.y = (x2 + 1) 3√x2 + 2
Differentiate.f(t) = 2t/2 + √t
Differentiate the function.y = ax2 + bx + c
Find the derivative of the function.y = (x2 + 1/x2 – 1)3
Differentiate the function.g(t) = t – √t/t2/3
Differentiate the function.y = √x (x – 1)
Find the derivative of the function.y = e–5x cos 3x
Differentiate.f(x) = A/B + Cex
Find the derivative of the function.y = ex cos x
Differentiate.f(x) = 1 – xex/x + ex

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