Final answer to the problem
$e^{ax}\left(a\sin\left(bx\right)+b\cos\left(bx\right)\right)$
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Step-by-step Solution
Learn how to solve product rule of differentiation problems step by step online. Find the derivative of e^(ax)sin(bx). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^{ax} and g=\sin\left(bx\right). 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 a function multiplied by a constant is equal to the constant times the derivative of the function. The derivative of the linear function is equal to 1.
Final answer to the problem
$e^{ax}\left(a\sin\left(bx\right)+b\cos\left(bx\right)\right)$
