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

Marvin Mccormick

Marvin Mccormick

Answered question

2021-10-08

Find the derivative of the following functions
y=23+sinx

Answer & Explanation

Adnaan Franks

Adnaan Franks

Skilled2021-10-09Added 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.

Jeffrey Jordon

Jeffrey Jordon

Expert2022-03-24Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?