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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\sec\left(x\right)$ and $g=1+\sec\left(x\right)^{-111}$
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$\frac{d}{dx}\left(\sec\left(x\right)\right)\left(1+\sec\left(x\right)^{-111}\right)+\sec\left(x\right)\frac{d}{dx}\left(1+\sec\left(x\right)^{-111}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of sec(x)(1+sec(x)^(-111)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sec\left(x\right) and g=1+\sec\left(x\right)^{-111}. Taking the derivative of secant function: \frac{d}{dx}\left(\sec(x)\right)=\sec(x)\cdot\tan(x)\cdot D_x(x). The derivative of the linear function is equal to 1. The derivative of a sum of two or more functions is the sum of the derivatives of each function.