Basic Forms from Calculus I

A complete set of fill-in-the-blank practice flashcards covering all standard derivative rules from Calculus I.

The derivative rule for a constant function is $\frac{d}{dx}[k] =$ __________.

$$0$$

The derivative rule for a power function $u^n$ is $\frac{d}{dx}[u^n] =$ __________.

$$n u^{n-1} u'$$

The derivative rule for a constant multiple is $\frac{d}{dx}[k u] =$ __________.

$$k u'$$

The sum and difference derivative rule is $\frac{d}{dx}[u \pm v] =$ __________.

$$u' \pm v'$$

The product derivative rule is $\frac{d}{dx}[u v] =$ __________.

$$u v' + v u'$$

The quotient derivative rule is $\frac{d}{dx}\left[\frac{u}{v}\right] =$ __________.

$$\frac{v u' - u v'}{v^2}$$

The derivative rule for a general function $f(u)$ is $\frac{d}{dx}[f(u)] =$ __________.

$$f'(u) \cdot u'$$

The derivative rule for the natural exponential function is $\frac{d}{dx}[e^u] =$ __________.

$$e^u u'$$

The derivative rule for the natural logarithm function is $\frac{d}{dx}[\ln(u)] =$ __________.

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

The derivative rule for the sine function is $\frac{d}{dx}[\sin(u)] =$ __________.

$$\cos(u) u'$$

The derivative rule for the cosecant function is $\frac{d}{dx}[\csc(u)] =$ __________.

$$-\csc(u) \cot(u) u'$$

The derivative rule for the cosine function is $\frac{d}{dx}[\cos(u)] =$ __________.

$$-\sin(u) u'$$

The derivative rule for the secant function is $\frac{d}{dx}[\sec(u)] =$ __________.

$$\sec(u) \tan(u) u'$$

The derivative rule for the tangent function is $\frac{d}{dx}[\tan(u)] =$ __________.

$$\sec^2(u) u'$$

The derivative rule for the cotangent function is $\frac{d}{dx}[\cot(u)] =$ __________.

$$-\csc^2(u) u'$$

The derivative rule for the inverse sine function is $\frac{d}{dx}[\sin^{-1}(u)] =$ __________.

$$\frac{u'}{\sqrt{1-u^2}}$$

The derivative rule for the inverse tangent function is $\frac{d}{dx}[\tan^{-1}(u)] =$ __________.

$$\frac{u'}{1+u^2}$$

The derivative rule for the inverse secant function is $\frac{d}{dx}[\sec^{-1}(u)] =$ __________.

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