Derivative Functions

$$\frac{d}{du}(a^{u})$$

$$a^{u}\ln a\cdot u^{\prime}$$

$$\frac{d}{du}(e^{u})$$

$$e^{u}\cdot u^{\prime}$$

$$\frac{d}{du}(\log_{a}u)$$

$$\frac{1}{u\ln a}\cdot u^{\prime}$$

$$\frac{d}{du}(\ln u)$$

$$\frac{1}{u}\cdot u^{\prime}$$

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

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

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

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