Derivatives of Trigonometric, Inverse Trigonometric, Exponential, and Logarithmic Functions

A set of vocabulary flashcards covering basic derivatives of trigonometric, inverse trigonometric, exponential, and logarithmic functions.

Derivative of $\sin(x)$

$$\cos(x)$$

Derivative of $\cos(x)$

$$-\sin(x)$$

Derivative of $\tan(x)$

$$\sec^2(x)$$

Derivative of $\cot(x)$

$$-\csc^2(x)$$

Derivative of $\sec(x)$

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

Derivative of $\csc(x)$

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

Derivative of $\sin^{-1}(x)$ / $\arcsin(x)$

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

Derivative of $\cos^{-1}(x)$ / $\arccos(x)$

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

Derivative of $\tan^{-1}(x)$ / $\arctan(x)$

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

Derivative of $\cot^{-1}(x)$ / \arccot(x)

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

Derivative of $\sec^{-1}(x)$ / \arcsec(x)

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

Derivative of $\csc^{-1}(x)$ / \arccsc(x)

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

Derivative of $e^x$

$$e^x$$

Derivative of $e^u$

$$e^u u'$$

Derivative of $a^x$

$$a^x \ln(a)$$

Derivative of $a^u$

$$a^u \ln(a) u'$$

Derivative of $\ln(x)$

$$\frac{1}{x}$$

Derivative of $\ln(|x|)$

$$\frac{1}{x}$$

Derivative of $\ln(u)$

$$\frac{u'}{u}$$

Derivative of $\log_a(x)$

$$\frac{1}{x \ln(a)}$$

Derivative of $\log_a(u)$

$$\frac{u'}{u \ln(a)}$$