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Question

If x=log(1+t2) and y=ttan1t. Then, dydx is equal to

A
ex1
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B
t21
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C
ex12
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D
exy
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Solution

The correct option is C ex12
Differentiating wrt 't'
dxdt=ddt(log(1+t2))=11+t22t=2t1+t2

dydt=ddt(ttan1t)=111+t2=t21+t2

dydx=t2/(1+t2)2t/(1+t2)=t2

x=log(1+t2)

ex=1+t2

t=ex1

t2=ex12

dydx=ex12.

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