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

Vocabulary flashcards covering differentiation rules for trigonometric, inverse trigonometric, exponential, and logarithm functions.

∫ sin(x) dx

-cos(x) + C

∫ cos(x) dx

sin(x) + C

∫ tan(x) dx

ln|sec(x)| + C

∫ cot(x) dx

ln|sin(x)| + C

∫ sec(x) dx

ln|sec(x) + tan(x)| + C

∫ csc(x) dx

ln|csc(x) - cot(x)| + C

∫ sec²(x) dx

tan(x) + C

∫ csc²(x) dx

-cot(x) + C

∫ sec(x)tan(x) dx

sec(x) + C

∫ csc(x)cot(x) dx

-csc(x) + C

$$\int \sin(x)\,dx$$

$$-\cos(x) + C$$

$$\int \cos(x)\,dx$$

$$\sin(x) + C$$

$$\int \tan(x)\,dx$$

$$\ln|\sec(x)| + C$$

$$\int \cot(x)\,dx$$

$$\ln|\sin(x)| + C$$

$$\int \sec(x)\,dx$$

$$\ln|\sec(x) + \tan(x)| + C$$

$$\int \csc(x)\,dx$$

$$\ln|\csc(x) - \cot(x)| + C$$

$$\int \sec^2(x)\,dx$$

$$\tan(x) + C$$

$$\int \csc^2(x)\,dx$$

$$-\cot(x) + C$$

$$\int \sec(x)\tan(x)\,dx$$

$$\sec(x) + C$$

$$\int \csc(x)\cot(x)\,dx$$

$$-\csc(x) + C$$

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

$$\cos(x)$$

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

$$-\sin(x)$$

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

$$\sec^2(x)$$

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

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

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

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

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

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

$$\frac{d}{dx}(\sin^{-1}(x))$$

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

$$\frac{d}{dx}(\cos^{-1}(x))$$

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

$$\frac{d}{dx}(\tan^{-1}(x))$$

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

$$\frac{d}{dx}(\cot^{-1}(x))$$

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

$$\frac{d}{dx}(\sec^{-1}(x))$$

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

$$\frac{d}{dx}(\csc^{-1}(x))$$

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

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

$$e^x$$

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

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

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

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