Final Answer
Step-by-step Solution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\sec\left(e^x\right)^2$ and $g=e^x$
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$e^x\frac{d}{dx}\left(\sec\left(e^x\right)^2\right)+\frac{d}{dx}\left(e^x\right)\sec\left(e^x\right)^2$
Learn how to solve differential calculus problems step by step online. Find the derivative of sec(e^x)^2e^x. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sec\left(e^x\right)^2 and g=e^x. 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(e^x\right)), you can add the exponents.