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The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
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$2\sec\left(x+1\right)\frac{d}{dx}\left(\sec\left(x+1\right)\right)$
Learn how to solve problems step by step online. Find the derivative of d/dx(sec(x+1)^2). 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 two powers that have the same base (\sec\left(x+1\right)), you can add the exponents. The derivative of a sum of two or more functions is the sum of the derivatives of each function.