Calculus: trig derivatives Flashcards | Quizlet

What is the derivative of $\sin(x)$?

$$\cos(x)$$

What is the derivative of $\cos(x)$?

$$-\sin(x)$$

What is the derivative of $\tan(x)$?

$$\sec^2(x)$$

What is the derivative of $\cot(x)$?

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

What is the derivative of $\sec(x)$?

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

What is the derivative of $\csc(x)$?

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

What is the derivative of $\arcsin(x)$?

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

What is the derivative of $\arccos(x)$?

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

What is the derivative of $\arctan(x)$?

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

What is the derivative of $\text{arccot}(x)$?

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

What is the derivative of $\text{arcsec}(x)$?

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

What is the derivative of $\text{arccsc}(x)$?

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

Using the chain rule, what is $\frac{d}{dx}(\sin(u))$?

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

Using the chain rule, what is $\frac{d}{dx}(\cos(u))$?

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

Using the chain rule, what is $\frac{d}{dx}(\tan(u))$?

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

Using the chain rule, what is $\frac{d}{dx}(\cot(u))$?

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

Using the chain rule, what is $\frac{d}{dx}(\sec(u))$?

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

Using the chain rule, what is $\frac{d}{dx}(\csc(u))$?

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

What is the derivative of $\sin^2(x)$?

$$2\sin(x)\cos(x)$$

What is the derivative of $\cos^2(x)$?

$$-2\cos(x)\sin(x)$$

What is the derivative of the product $x \sin(x)$?

$$\sin(x) + x \cos(x)$$

What is the derivative of the quotient $\frac{\sin(x)}{x}$?

$$\frac{x\cos(x) - \sin(x)}{x^2}$$

What is the derivative of the composite function $\sin(\cos(x))$?

$$-\cos(\cos(x))\sin(x)$$

What is the derivative of $\sqrt{\sin(x)}$?

$$\frac{\cos(x)}{2\sqrt{\sin(x)}}$$

What is the derivative of $\ln(\sec(x))$?

$$\tan(x)$$