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Hello Mr. Ahmed,

I have a multiple choice question and I am getting the derivative, but my answer choice is not listed in the problem. Hereis the problem I a struggling with:

If tan(xy)=x, then dy/dx=

A. (1-ytan(xy)sec(xy))/(xtan(xy)sec(xy))

B. (sec^2(xy)-y)/x

C. cos^2(xy)

D. (cos^2(xy))/x

E. (cos^2(xy)-y)/x

Thank you so much for your time!

Nikita

Hi Nikita,

To make it easier, let z = xy

Now,

tan(z) = x

differentiating, we get

secē(z) . dz/dx = 1

but from z = xy

dz/dx = x.dy/dx + y

Therefore,

secē(xy) . (x.dy/dx + y) = 1

x.dy/dx + y = 1/secē(xy)

x.dy/dx + y = cosē(xy)

x.dy/dx = cosē(xy) - y

dy/dx = [cosē(xy) - y] / x

Regards

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