Calculus 1 Basic Differentiation Rules: Sum and Difference Rules

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

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

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

300x^2(x^3 - 3)^99 * 3x^2

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

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

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

(5/2)x^(3/2)

Given y = √x * e^(2x), what is dy/dx?

(e^(2x) + 2√x * e^(2x)) / (2√x)

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

(e^(3x)(3 - x)) / x^2

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

(1/x)

For y = cos(πx), what is dy/dx?

-πsin(πx)

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

-4πsec²(4π/x)

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

-5sin(x)e^(5cos(x))

Learn about the basic differentiation rules in Calculus 1, specifically the Sum and Difference Rules. Understand how to evaluate the derivative of functions and derive formulas to determine the derivatives of a function that involve more than a single term.

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