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Derivatives (Foundations)

Core skills for this exam family.

Phase 2 · AP Calculus

Foundations Standard Advanced

Derivatives: core idea

\frac{d}{dx}x^n=nx^{n-1}

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Example problem: hint and answer

If $f(x)=x^2+3x$ , find $f'(2)$ .

Hint: Power rule. Answer: 7.

Practice (9 problems — type your answers)

1. If $f(x)=\sin x$ , find $f'(0)$ .
2. If $f(x)=e^x$ , find $f'(0)$ .
3. If $f(x)=\ln x$ , find $f'(1)$ .
4. If $f(x)=x^3$ , find $f'(1)$ .
5. If $f(x)=\sqrt{x}$ , find $f'(4)$ .
6. If $f(x)=1/x$ , find $f'(1)$ .
7. If $f(x)=\cos x$ , find $f'(0)$ .
8. If $f(x)=5x-2$ , find $f'(7)$ .
9. If $f(x)=|x|$ , is $f'(0)$ defined? Type $0$ for no, $1$ for yes.

Derivatives Practice Problems — Foundations