Examples
Differentiating x³ sin x with the product rule
The rule said first, each factor differentiated on its own line, then the two put together into the final answer.
- 0:46
- Maths problems
- Narrated by Erinome
- English
Made from a prompt
Differentiate y = x³ sin x.
Video transcript
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.
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