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differentiate the following function with respect to x (1)cos^-1(x/sqrt(x^2+a^2)) (2)sin^-1(sinx + cos x/sqrt(2)), -3pi/4 (3)cos^-1(cos x + sin x/sqrt(2)), -pi/4 (4)tan^-1(x/1+sqrt(1-x^2)), -1

differentiate the following function with respect to x
(1)cos^-1(x/sqrt(x^2+a^2))
(2)sin^-1(sinx + cos x/sqrt(2)), -3pi/4
(3)cos^-1(cos x + sin x/sqrt(2)), -pi/4
(4)tan^-1(x/1+sqrt(1-x^2)), -1

Grade:12

2 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago


Y=cos-1x/v(x2+a2)



Dy/dx=-[1/v1-{x/v(x2+a2)}2].[{v(x2+a2).1-x.2x/v(x2+a2)}/(x2+a2)]



=-a/(x2+a2)

Thanks & Regards

Rinkoo Gupta

AskIITians Faculty

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hi
I'll solve only first question for the rest make another post.
Substitue to get the answer.

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

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