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 $f=x^3$ and $g=e^{3x}\sin\left(x\right)$
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$\frac{d}{dx}\left(x^3\right)e^{3x}\sin\left(x\right)+x^3\frac{d}{dx}\left(e^{3x}\sin\left(x\right)\right)$
Learn how to solve problems step by step online. Find the derivative of x^3e^(3x)sin(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^3 and g=e^{3x}\sin\left(x\right). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^{3x} and g=\sin\left(x\right). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}.
