How do you differentiate y=xe^x?

Armani Stuart

Armani Stuart

Answered question

2023-02-17

How to differentiate y = x e x ?

Answer & Explanation

Rory Hess

Rory Hess

Beginner2023-02-18Added 10 answers

We using the product rule.
The product rule:
If u and v are differentiable functions of x, and f = u v , then f = u v + u v , where the apostrophe denotes the derivative with respect to x.
In the above question, we can see that x e x is a product of x and e x , both which are elementary functions.
Hence,
d d x ( x e x ) = d d x ( x ) e x + x d d x ( e x )
= ( 1 ) e x + x ( e x )
= ( 1 + x ) e x

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