What is derivative of \frac{x}{2-\tan x}

Daanish Wilcox

Daanish Wilcox

Answered question

2022-03-01

What is derivative of
x2tanx

Answer & Explanation

Toby Morris

Toby Morris

Beginner2022-03-02Added 3 answers

y=(x2tanx)=x(2tanx)x(2tanx)(2tanx)2
=2tanxx(tanx)(2tanx)2
=2tanx+xcos2x(2tanx)2
=2cos2xsinxcosx+xcos2x(2tanx)2
ushukela7wb

ushukela7wb

Beginner2022-03-03Added 3 answers

Using the quotient rule:
y=ddx(x)(2tanx)xddx(2tanx)(2tanx)2
Now
ddx(2tanx)=ddx(2)ddx(tanx)=0(sec2x)=sec2x
And clearly ddx(x)=1
y=1(2tanx)(x(sec2x))44tanx+tan2x=2tanx+xsec2x44tanx+tanx2

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