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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\left(9x^3+1\right)^2$ and $g=\sin\left(5x\right)$
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$\frac{d}{dx}\left(\left(9x^3+1\right)^2\right)\sin\left(5x\right)+\left(9x^3+1\right)^2\frac{d}{dx}\left(\sin\left(5x\right)\right)$
Learn how to solve problems step by step online. Find the derivative of (9x^3+1)^2sin(5x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(9x^3+1\right)^2 and g=\sin\left(5x\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)}. The derivative of the linear function times a constant, is equal to the constant.