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differentiate tan^-1(x-1/x+1) with respect to sin^-1(3x-4x^3), if -1/2

differentiate tan^-1(x-1/x+1) with respect to sin^-1(3x-4x^3), if -1/2

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
8 years ago

Y=tan-1((x-1)/(x+1))

Dy/dx=[1/{1+((x-1)/(x+1))2}].[(x+1).1-(x-1).1]/(x+1)2

=[1/{(x+1)2+(x-1)2}].2

=2/2(x2+1)=1/(1+x2)

Let z=sin-1(3x-4x3)

=3sin-1x

Dz/dx=3/v(1-x2)

Then dy/dz=(dy/dx)/(dz/dx)={1/(1+x2)}/{3/v(1-x2)}

=v(1-x2)/3(1+x2) Ans.

Thanks & Regards

Rinkoo Gupta

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