Final Answer
$4\sec\left(x\right)^{4}\tan\left(x\right)$
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Step-by-step Solution
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Simplifying
$\frac{d}{dx}\left(\sec\left(x\right)^{4}\right)$
Learn how to solve power rule for derivatives problems step by step online.
$\frac{d}{dx}\left(\sec\left(x\right)^{4}\right)$
Learn how to solve power rule for derivatives problems step by step online. Find the derivative of sec(x)^2sec(x)^2. Simplifying. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Taking the derivative of secant function: \frac{d}{dx}\left(\sec(x)\right)=\sec(x)\cdot\tan(x)\cdot D_x(x). When multiplying exponents with same base you can add the exponents: 4\frac{d}{dx}\left(x\right)\sec\left(x\right)^{3}\sec\left(x\right)\tan\left(x\right).
Final Answer
$4\sec\left(x\right)^{4}\tan\left(x\right)$