Final answer to the problem
Step-by-step Solution
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- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x^{3x}$ and $g=e^{5x}\mathrm{sinh}\left(4x\right)$
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$\frac{d}{dx}\left(x^{3x}\right)e^{5x}\mathrm{sinh}\left(4x\right)+x^{3x}\frac{d}{dx}\left(e^{5x}\mathrm{sinh}\left(4x\right)\right)$
Learn how to solve differential equations problems step by step online. Find the derivative of x^(3x)sinh(4x)e^(5x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^{3x} and g=e^{5x}\mathrm{sinh}\left(4x\right). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\mathrm{sinh}\left(4x\right) and g=e^{5x}. Applying the derivative of the exponential function. The derivative of the linear function times a constant, is equal to the constant.