IXL - Find derivatives using the product rule II (Calculus practice)

Find the derivative of

(

)

(

)

′

(

)

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Learn with an example

question

Find the derivative of

(

)

(

)

′

(

)

key idea

The product rule says that

[

(

)

(

)

]

′

(

)

(

)

(

)

′

(

)

whenever

(

)

and

(

)

are differentiable.

Common derivatives

u ( x )	u ′ ( x )
x n	n x n – 1
e x	e x
e k x	k e k x

solution

The function

(

)

is the sum of the functions

and

Rewrite

′

(

)

as the sum of two simpler derivatives.

′

(

)

(

)

′

(

)

′

(

)

′

Now, use the product rule to find each simpler derivative.

(

)

′

(

)

′

(

)

′

(

)

(

)

(

)

′

(

)

′

(

)

′

(

)

(

)

Finally, add the results.

′

(

)

(

)

′

(

)

′

(

)

(

)

So,

′

(

)

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