CLEP Calculus Basic Derivatives/Antiderivatives

$$\frac{\mathrm{d}}{\mathrm{d}x}(c)$$

$$0$$

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^n)$$

$$nx^{n-1}$$

$$\frac{\mathrm{d}}{\mathrm{d}x}(e^x)$$

$$e^x$$

$\frac{\mathrm{d}}{\mathrm{d}x}(\ln(x))$

$\frac{1}{x}$

$\frac{\mathrm{d}}{\mathrm{d}x}(\sin(x))$

$\cos(x)$

$\frac{\mathrm{d}}{\mathrm{d}x}(\cos(x))$

$-\sin(x)$

$\frac{\mathrm{d}}{\mathrm{d}x}(\tan(x))$

$\sec^2(x)$

$\frac{\mathrm{d}}{\mathrm{d}x}(\sec(x))$

$\sec(x)\tan(x)$

$\frac{\mathrm{d}}{\mathrm{d}x}(\csc(x))$

$-\csc(x)\cot(x)$

$\frac{\mathrm{d}}{\mathrm{d}x}(\cot(x))$

$-\csc^2(x)$

$\frac{\mathrm{d}}{\mathrm{d}x}(a^x)$

$a^x \ln(a)$

$\frac{\mathrm{d}}{\mathrm{d}x}(\arcsin(x))$

$\frac{1}{\sqrt{1-x^2}}$

$\frac{\mathrm{d}}{\mathrm{d}x}(\arctan(x))$

$\frac{1}{1+x^2}$

$\int x^n \mathrm{d}x$

$\frac{x^{n+1}}{n+1} + C$

$\int \frac{1}{x} \mathrm{d}x$

$\ln|x| + C$

$\int e^x \mathrm{d}x$

$e^x + C$

$\int \cos(x) \mathrm{d}x$

$\sin(x) + C$

$\int \sin(x) \mathrm{d}x$

$-\cos(x) + C$

$\int \sec^2(x) \mathrm{d}x$

$\tan(x) + C$

$\int \sec(x)\tan(x) \mathrm{d}x$

$\sec(x) + C$

$\int \csc^2(x) \mathrm{d}x$

$-\cot(x) + C$

$\int \csc(x)\cot(x) \mathrm{d}x$

$-\csc(x) + C$

$\int a^x \mathrm{d}x$

$\frac{a^x}{\ln(a)} + C$

$\int \frac{1}{\sqrt{1-x^2}} \mathrm{d}x$

$\arcsin(x) + C$

$\int \frac{1}{1+x^2} \mathrm{d}x$

$\arctan(x) + C$