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

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

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

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

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

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.

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

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

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

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

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

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