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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=
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$\frac{d}{dx}\left(x^{-3}\right)e^x+x^{-3}\frac{d}{dx}\left(e^x\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of xy+4y=x^(-3)e^x. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Applying the derivative of the exponential function. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.