Question
Asked Oct 19, 2019

Differentiate the function 

9. g(x) = In(xe 2x)
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9. g(x) = In(xe 2x)

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check_circleExpert Solution
Step 1

The given function is shown below:

-2x
g(x)= In (xe)
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-2x g(x)= In (xe)

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Step 2

Concept used:

1. Chain rule of derivative
d
g(u)
dx
dg du
du d
2. Product rule of derivative
d
dv
du
dx
dx
dx
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1. Chain rule of derivative d g(u) dx dg du du d 2. Product rule of derivative d dv du dx dx dx

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Step 3

Now in the given function g(x) substitute xe-2x = u thus g = ln (u).

Diffe...

dg dg du
dx
du dx
d
d
(In u)
dx
du
d
d
-2x
1
{using product rule
е
e
х
dx
dx
1
-2e +e2
1
-2xe
_
и
1
(-2x +1)e2
и
1
fu=x-e*
(1-2x)e
-2 x
X e
(1-2x)
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dg dg du dx du dx d d (In u) dx du d d -2x 1 {using product rule е e х dx dx 1 -2e +e2 1 -2xe _ и 1 (-2x +1)e2 и 1 fu=x-e* (1-2x)e -2 x X e (1-2x)

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Tagged in

Math

Calculus

Derivative