Derivatives & Integrals

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\frac{d}{\differentialD x}\left(cf\left(x\right)\right)=

$$cf^{\prime}\left(x\right)$$

\frac{d}{\differentialD x}\left(x^{n}\right)=

$$nx^{n-1}$$

\frac{d}{\differentialD x}\left(f\left(x\right)\cdot g\left(x\right)\right)=

$$f^{\prime}\left(x\right)\cdot g\left(x\right)+f\left(x\right)\cdot g^{\prime}\left(x\right)$$

\frac{d}{\differentialD x}\left(\frac{f\left(x\right)}{g\left(x\right)}\right)=

$$\frac{\left(f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g^{\prime}\left(x\right)\right)}{\left(g^{}\left(x\right)\right)^2}$$

\frac{d}{\differentialD x}\left\lbrack f\left(g\left(x\right)\right)\right\rbrack=

$$f^{\prime}\left(g\left(x\right)\right)\cdot g^{\prime}\left(x\right)$$

\frac{d}{\differentialD x}\left(f\left(x\right)\pm g\left(x\right)\right)=

$$f^{\prime}\left(x\right)\pm g^{\prime}\left(x\right)$$

\frac{d}{\differentialD x}\left(c\right)=

$$0$$

\frac{d}{\differentialD x}\left(e^{g\left(x\right)}\right)=

$$g^{\prime}\left(x\right)\cdot e^{g\left(x\right)}$$

\frac{d}{\differentialD x}\left\lbrack\ln\left(g\left(x\right)\right)\right\rbrack=

$$\frac{g^{\prime}\left(x\right)}{g\left(x\right)}$$

\frac{d}{\differentialD x}\left\lbrack\sin\left(x\right)\right\rbrack=

$$\cos\left(x\right)$$

\frac{d}{\differentialD x}\left\lbrack\cos\left(x\right)\right\rbrack=

$$-\sin\left(x\right)$$

\frac{d}{\differentialD x}\left\lbrack\tan\left(x\right)\right\rbrack=

$$\sec^2\left(x\right)$$

\frac{d}{\differentialD x}\left\lbrack\csc\left(x\right)\right\rbrack=

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

\frac{d}{\differentialD x}\left\lbrack\sec\left(x\right)\right\rbrack=

$$\sec\left(x\right)\tan\left(x\right)$$

\frac{d}{\differentialD x}\left\lbrack\cot\left(x\right)\right\rbrack=

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