help@askiitians.com

1800-150-456-789

Differential Calculus> differentiate the following function with...

question mark

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

taniska , 10 Years ago

Grade 12

2 Answers

Arun Kumar

Last Activity: 10 Years ago

Hi

I'll solve only first question for the rest make single post with single question.

applying chain rule.

$\\\frac{d}{dx}\left(\arcsin\left(\frac{1}{\sqrt{1+x^2}}\right)\right) \\=\frac{d}{du}\left(\arcsin \left(u\right)\right)\frac{d}{dx}\left(\frac{1}{\sqrt{1+x^2}}\right) \\=\frac{1}{\sqrt{1-u^2}}\left(-\frac{x}{\left(x^2+1\right)^{\frac{3}{2}}}\right) \\=\frac{1}{\sqrt{1-\left(\frac{1}{\sqrt{1+x^2}}\right)^2}}\left(-\frac{x}{\left(x^2+1\right)^{\frac{3}{2}}}\right) \\=-\frac{\text{sgn}\left(x\right)}{x^2+1} \\&sgn(x)=\frac{x}{|x|}&$

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

Rinkoo Gupta

Last Activity: 10 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

Provide a better Answer & Earn Cool Goodies

Enter text here...

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

Ask a Doubt

Get your questions answered by the expert for free

Enter text here...

the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution tomove once over to level a playground. find the area of the playground in square m?

differential calculus

1 Answer Available

Last Activity: 2 Years ago

Find dy/DX when y=x^sinx+sin-1√x. Please give me the solution of this problem.

differential calculus

0 Answer Available

Last Activity: 2 Years ago

If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.

differential calculus

0 Answer Available

Last Activity: 2 Years ago

Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.

differential calculus

0 Answer Available

Last Activity: 2 Years ago

Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin Cwhere A + B + C = T(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.

differential calculus

0 Answer Available

Last Activity: 2 Years ago

View all Questions