How do I go about solving this derivative

Destinee Bryan

Destinee Bryan

Answered question

2022-04-14

How do I go about solving this derivative of inverse tangent?
f(x)=8tan1(yx)ln(x2+y2)

Answer & Explanation

carlosegundoacyg

carlosegundoacyg

Beginner2022-04-15Added 10 answers

Since
f(x)=8tan1(yx)ln(x2+y2)
since
8ddxtan1(x)=811+x2
would
8ddxtan1(yx)=8(11+(yx)2)
ddx(tan1(yx))=81+(yx)2ddx(yx)
Recall that
ddxtan1(g(x))=11+(g(x))2g(x)
Here,
g(x)=yxg(x)=yx2
For the second term, use a nice property of logarithms:
lnx2+y2=ln(x2+y2)12=12ln(x2+y2)
Now, when differentiating the second term, don't forget the chain rule for this term too.
ddx(12ln(x2+y2))=121x2+y2ddx(x2+y2)
And remember, y is being used as a constant.

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