Second derivatives Find d^{2}y/dx^{2}*x + y = sin^{y}

Tyra

Tyra

Answered question

2021-10-03

Second derivatives Find d2ydx2x+y=siny

Answer & Explanation

Malena

Malena

Skilled2021-10-04Added 83 answers

Step 1
Given that
x+y=siny...(1)
Step 2
Differentiate (1) with respect to x,
ddx(x+y)=ddx(siny)
1+dydx=cosydydx
dydx(cosy1)=1
dydx=1cosy1...(2)
Step 3
Again differentiate (2) with respect to x,
d2ydx2=ddx(1cosy1)
=(cosy1)ddx(1)(1)ddx(cosy1)(cosy1)2
=(cosy1)(0)(sinydydx)(cosy1)2
=sinydydx(cosy1)2
=siny(1(cosy1))(cosy1)2 [Using (2)]
=siny(cosy1)3
Step 4
Hence
d2ydx2=siny(cosy1)3
Jeffrey Jordon

Jeffrey Jordon

Expert2022-02-01Added 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?