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

Vocabulary flashcards covering the derivative rules for trigonometric, inverse trigonometric, exponential, and logarithmic functions using the chain rule.

Derivative of $\sin(u)$

$$\cos(u) \frac{du}{dx}$$

Derivative of $\cos(u)$

$$-\sin(u) \frac{du}{dx}$$

Derivative of $\tan(u)$

$$\sec^2(u) \frac{du}{dx}$$

Derivative of $\cot(u)$

$$-\csc^2(u) \frac{du}{dx}$$

Derivative of $\sec(u)$

$$\sec(u) \tan(u) \frac{du}{dx}$$

Derivative of $\csc(u)$

$$-\csc(u) \cot(u) \frac{du}{dx}$$

Derivative of $\sin^{-1}(u)$

$$\frac{1}{\sqrt{1-u^2}} \frac{du}{dx}$$

Derivative of $\cos^{-1}(u)$

$$-\frac{1}{\sqrt{1-u^2}} \frac{du}{dx}$$

Derivative of $\tan^{-1}(u)$

$$\frac{1}{1+u^2} \frac{du}{dx}$$

Derivative of $\cot^{-1}(u)$

$$-\frac{1}{1+u^2} \frac{du}{dx}$$

Derivative of $\sec^{-1}(u)$

$$\frac{1}{|u|\sqrt{u^2-1}} \frac{du}{dx}$$

Derivative of $\csc^{-1}(u)$

$$-\frac{1}{|u|\sqrt{u^2-1}} \frac{du}{dx}$$

Derivative of $e^u$

$$e^u \frac{du}{dx}$$

Derivative of $a^u$

$$a^u \ln(a) \frac{du}{dx}$$

Derivative of $\log_a(u)$

$$\frac{1}{u \ln(a)} \frac{du}{dx}$$

Derivative of $\ln(u)$

$$\frac{1}{u} \frac{du}{dx}$$