Final Answer
$y^{\prime}=\sec\left(x\right)\tan\left(x\right)$
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Step-by-step Solution
Problem to solve:
$\frac{d}{dx}\left(y=\sec\left(x\right)\right)$
Specify the solving method
1
Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable
$\frac{d}{dx}\left(y\right)=\frac{d}{dx}\left(\sec\left(x\right)\right)$
Learn how to solve implicit differentiation problems step by step online.
$\frac{d}{dx}\left(y\right)=\frac{d}{dx}\left(\sec\left(x\right)\right)$
Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative d/dx(y=sec(x)). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function is equal to 1. Taking the derivative of secant function: \frac{d}{dx}\left(\sec(x)\right)=\sec(x)\cdot\tan(x)\cdot D_x(x).
Final Answer
$y^{\prime}=\sec\left(x\right)\tan\left(x\right)$