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• Trigonometry
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Derivative of secx formula

Formula

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

The differentiation or derivative of secant function with respect to a variable is equal to the product of secant and tangent functions. This derivative formula is read as the derivative of $\sec{x}$ function with respect to $x$ is equal to the product of $\sec{x}$ and $\tan{x}$.

Introduction

Assume $x$ is a variable, then the secant function is written as $\sec{x}$ in mathematical form as per trigonometry. The derivative of the secant function with respect to $x$ is written as the following mathematical form.

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

In mathematics, the differentiation of the $\sec{x}$ function with respect to $x$ can be written as $\dfrac{d{\,(\sec{x})}}{dx}$ and also simply written as ${(\sec{x})}’$.

Other form

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

$(1) \,\,\,$ $\dfrac{d}{dh}{\, (\sec{h})} \,=\, \sec{h}\tan{h}$

$(2) \,\,\,$ $\dfrac{d}{dw}{\, (\sec{w})} \,=\, \sec{w}\tan{w}$

$(3) \,\,\,$ $\dfrac{d}{dy}{\, (\sec{y})} \,=\, \sec{y}\tan{y}$

Proof

Learn how to prove the derivative of the secant function by first principle in differential calculus.