Calc Unit 2 Derivative Rules

Power Rule

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

Constant Rule

$$\frac{d}{dx}(c)=0$$

Constant Multiple Rule

$$\frac{d}{dx}[cf(x)]=cf'(x)$$

Addition Rule

$$\frac{d}{dx}[f(x)+g(x)]=f'(x)+g'(x)$$

Subtraction Rule

$$\frac{d}{dx}[f(x)-g(x)]=f'(x)-g'(x)$$

Product Rule

$$\frac{d}{dx}[f(x)g(x)]=f'(x)g(x)+f(x)g'(x)$$

Quotient Rule

$$\frac{d}{dx}\left[\frac{f(x)}{g(x)}\right]=\frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}$$

$$e^x$$

$$\frac{d}{dx}(e^x)=e^x$$

$$a^x$$

$$\frac{d}{dx}(a^x)=a^x\ln(a)$$

$$\ln(x)$$

$$\frac{d}{dx}[\ln(x)]=\frac{1}{x}$$

$$\log_a(x)$$

$$\frac{d}{dx}[\log_a(x)]=\frac{1}{x\ln(a)}$$

$$\sin(x)$$

$$\frac{d}{dx}[\sin(x)]=\cos(x)$$

$$\cos(x)$$

$$\frac{d}{dx}[\cos(x)]=-\sin(x)$$

$$\tan(x)$$

$$\frac{d}{dx}[\tan(x)]=\sec^2(x)$$

$$\sec(x)$$

$$\frac{d}{dx}[\sec(x)]=\sec(x)\tan(x)$$

$$\csc(x)$$

$$\frac{d}{dx}[\csc(x)]=-\csc(x)\cot(x)$$

$$\cot(x)$$

$$\frac{d}{dx}[\cot(x)]=-\csc^2(x)$$