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Derivative of tanx formula

Formula

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

The derivative or differentiation of tan function with respect to a variable is equal to square of the secant function. It is read as the derivative of $\tan{x}$ with respect to $x$ is equal to $\sec^2{x}$.

Introduction

If $x$ is taken as a variable, then the tangent function is written as $\tan{x}$ in mathematics. The derivative of the tan function with respect to $x$ is written mathematically in differential calculus as follows.

$\dfrac{d}{dx}{\, (\tan{x})}$

The derivative of $\tan{x}$ with respect to $x$ is also be expressed as $\dfrac{d{\,(\tan{x})}}{dx}$. It can also be written as ${(\tan{x})}’$ simply in calculus.

Other form

The differentiation of the tan function can be written in terms of any variable.

$(1) \,\,\,$ $\dfrac{d}{dg}{\, (\tan{g})} \,=\, \sec^2{g}$

$(2) \,\,\,$ $\dfrac{d}{dz}{\, (\tan{z})} \,=\, \sec^2{z}$

Proof

Learn how to derive the differentiation of the tan function from first principle in differential calculus.