Final answer to the problem
$e^t\sin\left(t\right)+e^t\cdot t\sin\left(t\right)+e^t\cdot t\cos\left(t\right)$
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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 te^tsin(t). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=t and g=e^t\sin\left(t\right). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^t and g=\sin\left(t\right). The derivative of the linear function is equal to 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)}.
Final answer to the problem
$e^t\sin\left(t\right)+e^t\cdot t\sin\left(t\right)+e^t\cdot t\cos\left(t\right)$
