Derivative (1st order)

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #141

Find the derivative of `sin^{-1}(2ax\sqrt{1-a^2\x^2})` w.r.t. `\sqrt{1-a^2\x^2}` where `-frac{1}{\sqrt{2}}\lt\ax\lt\frac{1}{\sqrt{2}}`

Question No: #142

Find `\frac{dy}{dz}` where `y=tan^{-1}(\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}})` and `z=cos^{-1}x^2`

Question No: #143

Find the derivative of `tan^{-1}(\frac{t}{\sqrt{1-t^2}})` with respect to `sec^{-1}(\frac{1}{2t^2-1})`

Question No: #144

Find the derivative of `tan^{-1]\frac{\sqrt{1+x^2}-1}{x}` with respect to `tan^{-1}x`

Question No: #145

Differentiate `tan^{-1}\frac{\sqrt{1+x^2}-1}{x}` w.r.t. `cos^{-1}(2x\sqrt{1-x^2})` at `x=0`

Question No: #146

Find the derivative of `tan^{-1}\frac{\sqrt{1+x^2}-1}{x}` with respect to `tan^{-1}\frac{2x\sqrt{1-x^2}}{1-2x^2}` at `x=0`

Question No: #147

Find the derivative of with `tan^{-1}\frac{2x\sqrt{1-x^2}}{1-2x^2}` with respect to `tan^{-1}\frac{\sqrt{1+x^2}-1}{x}` where `x\ne0`

Question No: #148

Show that the derivative of `cot^{-1}\frac{2\sqrt{1+x^2}-5\sqrt{1-x^2}}{5\sqrt{1+x^2}+2\sqrt{1-x^2}}` with respect to `cos^{-1]\sqrt{1-x^4}` is `-\frac{1}{2}`