# Derivatives of Algebraic functions

There are some standard results with algebraic functions and they are used as formulas in differential calculus to find the differentiation of algebraic functions.

### Derivative of Constant

The derivative of any constant with respect to a variable is equal to zero.

$\dfrac{d}{dx}{\, (c)} \,=\, 0$

### Derivative of Variable

The derivative of a variable with respect to same variable is equal to one.

$\dfrac{d}{dx}{\, (x)} \,=\, 1$

### Derivative of Square root

The derivative of square root of a variable with respect to same variable is equal to the quotient of one by two times the square root of the variable.

$\dfrac{d}{dx}{\, \sqrt{x}} \,=\, \dfrac{1}{2\sqrt{x}}$

### Derivative of Exponential functions

$(1) \,\,\,\,\,$ $\dfrac{d}{dx}{\, x^n} \,=\, nx^{n-1}$

$(2) \,\,\,\,\,$ $\dfrac{d}{dx}{\, e^x} \,=\, e^x$

$(3) \,\,\,\,\,$ $\dfrac{d}{dx}{\, a^x} \,=\, a^x\log{a}$

### Derivative of Log function

$\dfrac{d}{dx}{\, \log_{e}{(x)}} \,=\, \dfrac{1}{x}$

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