اشتقاق x³ sin x بقاعدة الضرب

In this video, we differentiate a product using the product rule.

Question one. Differentiate y equals x cubed sine x.

Let us solve it. Use the product rule: differentiate the first factor times the second, then add the first factor times the derivative of the second. The derivative of x cubed is three x squared, using the power rule.

The derivative of sine x is cosine x.

Substituting these derivatives gives three x squared times sine x plus x cubed times cosine x. Hence, d y by d x equals three x squared sine x plus x cubed cosine x.