Question 1

What is the derivative of x^n?

Accepted Answer

nx^(n-1). Multiply by the exponent, then subtract one from it. So the derivative of x^3 is 3x^2.

Question 2

What is the integral of 1/x?

Accepted Answer

ln|x| + C. The absolute value matters because ln is only defined for positive inputs, and 1/x exists for negative x too.

Question 3

When do I use the chain rule?

Accepted Answer

When you're differentiating a function inside another function — like sin(x^2) or (3x+1)^5. The chain rule multiplies the outside derivative by the inside derivative.

Function	Derivative
xⁿ	n·xⁿ⁻¹
sin x	cos x
cos x	−sin x
e^x	e^x
ln x	1/x

Function	Integral
xⁿ	xⁿ⁺¹/(n+1) + C
sin x	−cos x + C
cos x	sin x + C
e^x	e^x + C
1/x	ln\|x\| + C

Calculus 1 Cheat Sheet: Derivatives & Integrals

Common derivatives

Common integrals

Differentiation rules

Calculus 1 Cheat Sheet: Derivatives & Integrals

Common derivatives

Common integrals

Differentiation rules

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