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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 81 Points
10 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
10 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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