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

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

Grade:12

2 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hi
I'll solve only first question for the rest make single post with single question.
applying chain rule.

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

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago

Y=sin-1{1/v(1+x2)}

Dy/dx=[1/v1-{1/v(1+x2)}2].{-(1+x2)-3/2/2}

On simplifying we get

Dy/dx=-1/(1+x2)

Thanks & Regards

Rinkoo Gupta

AskIITians Faculty

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