Find the derivative of the following functions y=2^{3+\sin x}

Marvin Mccormick 2021-10-08 Answered
Find the derivative of the following functions
y=23+sinx
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Expert Answer

Adnaan Franks
Answered 2021-10-09 Author has 92 answers

Step 1
Consider the provided function,
y=23+sinx...(1)
Find the derivative of the above functions.
First, we taking log both the sides.
lny=ln(23+sinx)
Apply the log property ln(mn)=n ln(m).
So,
lny=ln(23+sinx)
lny=(3+sinx)ln(2)
Step 2
Now, the above equation differentiate with respect to x.
Apply the common derivative rule ddx(lnx)=1x1 and ddx(sinx)=cosx
ddx(lny)=ddx[(3+sinx)ln(2)]


1ydydx=ln(2)ddx[(3+sinx)]


1ydydx=ln(2)(0+cosx)


1ydydx=ln(2)cosx


dydx=yln(2)cosx
Step 3
Now, in the equation (1) we put the value of y in the above derivative.
We get,
dydx=(23+sinx)ln(2)cosx
=ln(2)(23+sinx)cosx
Hence.

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Jeffrey Jordon
Answered 2022-03-24 Author has 2027 answers

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