Find a formula for the derivative of the function
![\[ f(x) = x^4 \sin x. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-12cacb07d3a2d5fbeb5fbb9550d96404_l3.png "Rendered by QuickLaTeX.com")
By the product rule for derivatives, and the formulas for derivatives of polynomials and the derivative of sine, we have
![\[ f'(x) = 4x^3 \sin x + x^4 \cos x. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-183eba971ab96fc6885e21dbf3443b9f_l3.png "Rendered by QuickLaTeX.com")
Find a formula for the derivative of the function
By the product rule for derivatives, and the formulas for derivatives of polynomials and the derivative of sine, we have