Derivative (1st order)

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

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Question No: #101

If `y=1+\frac{a}{x-a}+\frac{bx}{(x-a)(x-b)}+\frac{cx^2}{(x-a)(x-b)(x-c)}` then show that `\frac{dy}{dx}=\frac{y}{x}[\frac{a}{a-x}+\frac{b}{b-x}+\frac{c}{c-x}]` where `x\nea,b,c`
Ans: N.A.
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Question No: #102

If `f(x)=(1+x)(1+x^2)(1+x^4)(1+x^8)` then find the value of `f'(1)`

Question No: #103

If `y=(1+x)(1+x^2)(1+x^4)\cdots(1+x^{2n})`, then find the value of `\frac{dy}{dx}` at `x=0`

Question No: #104

If `log(x^2+y^2)=2tan^{-1}(\frac{y}{x})`, then show that `\frac{dy}{dx}=\frac{x+y}{x-y}`

Question No: #105

If `y=sin^{-1}(\frac{5x+12\sqrt{1-x^2}}{13})`, then find `\frac{dy}{dx}`

Question No: #106

Find `\frac{dy}{dx}` where `y=cos^{-1}(\frac{x-1/x}{x+1/x})`

Question No: #107

Find `\frac{dy}{dx}` where `y=cos^{-1}(\frac{2\cosx-3\sinx}{\sqrt{13}})`

Question No: #108

If `y=2sin^{-1}\frac{x-2}{\sqrt{6}}-\sqrt{2+4x-x^2}`, then show that the value of `\frac{dy}{dx}` at `x=2` is `\frac{2}{\sqrt{6}}`

Question No: #109

Find `\frac{dy}{dx}` where `y=cos^{-1]2x+2cos^{-1}\sqrt{1-4x^2}`

Question No: #110

If `y=tan^{-1](\frac{cosx}{1+sinx})`, then find `\frac{dy}{dx}`