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 $f=e^{-x}$ and $g=\tan\left(e^x\right)$
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$\frac{d}{dx}\left(e^{-x}\right)\tan\left(e^x\right)+e^{-x}\frac{d}{dx}\left(\tan\left(e^x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of e^(-x)tan(e^x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^{-x} and g=\tan\left(e^x\right). The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}. Applying the derivative of the exponential function. When multiplying exponents with same base we can add the exponents.