Derivative (1st order)

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

Click on each question to see answer & solution.

Question No: #111

If `y=tan^{-1]\frac{cosx+sinx}{cosx-sinx}` then find the value of `\frac{dy}{dx}`

Question No: #112

If `y=tan^{-1}\frac{a\cosx-b\sinx}{b\cosx+a\sinx}` where `-\frac{\pi}{2}\lt\x\lt\frac{\pi}{2}` and `\frac{a}{b}tanx\gt-1`, then show that `\frac{dy}{dx}=-1`

Question No: #113

If `y=cot^{-1}\sqrt{\frac{1-sinx}{1+sinx}}` where `(0\lt\x\lt\frac{\pi}{2})`, then find `\frac{dy}{dx}`

Question No: #114

If `sin^{-1}(\frac{x^2-y^2}{x^2+y^2})=k` (where `k` is constant), then show that `\frac{dy}{dx}=\frac{y}{x}`
Ans: `y/x`
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Question No: #115

If `y=sin^{-1}\frac{a+b\cosx}{b+a\cosx}`, then prove that `\frac{dy}{dx}=-\frac{\sqrt{b^2-a^2}}{b+a\cosx}`

Question No: #116

If `y=cos^{-1}(8x^4-8x^2+1)` then show that `\frac{dy}{dx}+\frac{4}{\sqrt{1-x^2}}=0`

Question No: #117

If `x=cos^{-1}(8t^4-8t^2+1)` and `y=sin^{-1}(3t-4t^3)` where `(0\lt t \lt \frac{1}{2})` then find `\frac{dy}{dx}`

Question No: #118

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

Question No: #119

If `y=2\tan^{-1}\sqrt{\frac{x-a}{b-x}}` where `a\ltx\ltb`, then show that `(\frac{dy}{dx})^2+\frac{1}{(x-a)(x-b)}=0`

Question No: #120

If `y=tan^{-1}\frac{5-x}{1+5x}`, then find the value of `\frac{dy}{dx}`