Final answer to the problem
$x^2\left(3\cos\left(5x\right)-5x\sin\left(5x\right)\right)$
Got another answer? Verify it here!
Step-by-step Solution
Learn how to solve product rule of differentiation problems step by step online. Find the derivative of x^3cos(5x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^3 and g=\cos\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 cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). The derivative of the linear function times a constant, is equal to the constant.
Final answer to the problem
$x^2\left(3\cos\left(5x\right)-5x\sin\left(5x\right)\right)$
