Exponential :Exp and Num base

$$e^{4x}$$  

$$4e^{4x}$$  

$$4xe^{4x}$$  

$$e^{4x-1}$$  

$$5\sqrt[]{x}e^{\sqrt[]{x}}$$  

$$\frac{5\sqrt[]{x}}{2}e^{\sqrt[]{x}}$$  

$$\frac{5}{\sqrt[]{x}}e^{\sqrt[]{x}}$$  

$$\frac{5}{2\sqrt[]{x}}e^{\sqrt[]{x}}$$  

$$2e^{-x^3}$$  

$$-6x^2e^{-x^3}$$  

$$-2x^3e^{-x^3-1}$$  

$$\frac{2}{3e^{x^3}}$$  

$$\frac{12}{x}e^{\frac{2}{x}-1}$$  

$$-\frac{12}{x^2}e^{\frac{2}{x}}$$  

$$\frac{12}{x^2}e^{\frac{2}{x}}$$  

$$12e^{\frac{2}{x}}$$  

$$3^{2x}\ln9$$  

$$3^{2x}\left(2\ln3\right)$$  

$$3^{2x}\ln6$$  

$$3^{2x}\ln3$$  

$$x^25^{x^2-1}$$  

$$5^{x^2}\left(2x\ln5\right)$$  

$$5^{x^2}\ln\left(10x\right)$$  

$$5^{x^2}\ln5$$  

$$4^{\frac{1}{x}}\ln4$$  

$$\frac{1}{x}4^{\frac{1}{x}-1}$$  

$$\frac{-4^{\frac{1}{x}}}{x^2}\ln4$$  

$$4^{\frac{1}{x}}\ln4\left(\frac{1}{x}\right)$$

Power Rule

Direct

Quotient Rule

Product Rule

Power Rule

Direct

Quotient Rule

Product Rule

$$9xe^{3x}$$  

$$-6e^{3x}+9xe^{3x}$$  

$$-9xe^{3x}$$  

$$-2e^{3x}-3xe^{3x}$$  

Direct

Product Rule

Quotient Rule

Power Rule

$$\frac{-4+4x}{e^{2x}}$$  

$$\frac{-3+2x}{e^{2x}}$$  

$$\frac{-4x}{e^{2x}}$$  

$$-4e^{2x}+4xe^{2x}$$  

$$4^{x^2-2x\ }\ln4$$  

$$\left(2x\ln4\right)4^{x^2-2x}$$  

$$\left(2x\ln4-2\ln4\right)4^{x^2-2x}$$

$$\left(2x\ln4\right)4^{x^2-2x}$$

Direct

Product Rule

Quotient Rule

Power Rule

$$\frac{1}{3}e^{2x}\left(1-e\right)^{-\frac{2}{3}}$$  

$$-\frac{2}{3}e^{2x}\left(1-e^{2x}\right)^{-\frac{2}{3}}$$  

$$\frac{2}{3}e^{2x}\left(1-e^{2x}\right)^{-\frac{2}{3}}$$

$$-6e^{2x}\left(1-e^{2x}\right)^2$$