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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(e^x\right)x^{3x}+e^x\frac{d}{dx}\left(x^{3x}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of y=e^xx^(3x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. Applying the derivative of the exponential function. The derivative \frac{d}{dx}\left(x^{3x}\right) results in 3\left(\ln\left(x\right)+1\right)x^{3x}. Simplify the derivative.