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Calculus 1 Basic Differentiation Rules: Sum and Difference Rules

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Calculus 1 Basic Differentiation Rules: Sum and Difference Rules

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Questions and Answers

What is the derivative of the function y = (1 + 2x^4) / (1 - 2x^4) using the Chain Rule?

(8x^3) / (1 - 2x^4)
(16x^3) / (1 - 2x^4)^2 (correct)
(8x^3) / (1 - 2x^4)^2
(16x^3) / (1 - 2x^4)

If f(x) = x^3 - 3 and g(x) = x^3 - 3, what is the derivative of f(g(x))?

200x^2(x^3 - 3)^99 * 3x^2
300x^2(x^3 - 3)^99 * 3x^2 (correct)
300x^2(x^3 - 3)^98 * 3x^2
300x^2(x^3 - 3)^99 * 2x

If f(x) = x^4 - 2x^3 + 2x - 11 and g(x) = x^4 - 2x^3 + 2x - 11, what is f'(g(x))?

(3x^3 - x^2 + 1) / (x^4 - x^3 + 2x)
(2x^3 - 3x^2 + 1) / (x^4 - 2x^3 + 2x) (correct)
(3x^3 - 3x^2 + 1) / (x^4 - 2x^3 + 2x)
(2x^3 - x^2 + 1) / (x^4 - x^3 + 2x)

For a function y = x^(5/2), what is its derivative?

(5/2)x^(3/2) (A) Signup and view all the answers

Given y = √x * e^(2x), what is dy/dx?

(e^(2x) + 2√x * e^(2x)) / (2√x) (A) Signup and view all the answers

What is the derivative of y = e^(3x) / x?

(e^(3x)(3 - x)) / x^2 (A) Signup and view all the answers

If f(x) = ln(x), what is f'(x)?

(1/x) (C) Signup and view all the answers

For y = cos(πx), what is dy/dx?

-πsin(πx) (D) Signup and view all the answers

What is the derivative of y = tan(4π/x)?

-4πsec²(4π/x) (A) Signup and view all the answers

If f(x) = e^(5cos(x)), what is f'(x)?

-5sin(x)e^(5cos(x)) (D) Signup and view all the answers