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

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