If \sin x=e^y,0<x<\pi, what is dy/dx in terms of x?(A) -\tan x(B) -\cot x(C) \cot x(D) \tan x(E) \csc x

Wierzycaz

Wierzycaz

Answered question

2020-11-01

If sinx=ey,0<x<π, what is dy/dx in terms of x?
(A) tanx
(B) cotx
(C) cotx
(D) tanx
(E) cscx

Answer & Explanation

Gennenzip

Gennenzip

Skilled2020-11-02Added 96 answers

Answer is C
sinx=e
Then by applying natural logarithm:
lnsinx=lne
lnsinx=y
so, y=(1sinx)ddx(sinx)=(1sinx)(cos x)=cotx

Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-14Added 2605 answers

sinx=ey

ln(sinx)=y

d(ln(sinx))=dy

u=sinx

du=cosxdx

d(lnu)=dy

duu=dy

cosxsinxdx=dy

cotx=dydx

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