Question
Asked Nov 14, 2019
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Find the derivative of f(x)=(sinxcosx)1/2

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Expert Answer

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Step 1

Given the function,

f(x)(sinxcos x)
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f(x)(sinxcos x)

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Step 2

We have the identity

2sin rcosx sin(2x)
sin (2x)
sin xcosx=
2
sin(2x)
Then the function can be written as f(x) =
2
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2sin rcosx sin(2x) sin (2x) sin xcosx= 2 sin(2x) Then the function can be written as f(x) = 2

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Step 3

Differentiate the ab...

d sin (2x)
f'(x)=
dx
2
Let us apply the chain rule.
df (u)_df_du
dx
du dx
sin(2x
Let f u, where
2
df
Then,
1
1
du 2
2u2
du 2cos(2x)
cos(2x)
And
dic
2
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d sin (2x) f'(x)= dx 2 Let us apply the chain rule. df (u)_df_du dx du dx sin(2x Let f u, where 2 df Then, 1 1 du 2 2u2 du 2cos(2x) cos(2x) And dic 2

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Tagged in

Math

Calculus

Derivative

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