Derivative (1st order)

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

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Question No: #131

if `y=cot^{-1}(\frac{\sqrt{1+sinx}+\sqrt{1-sinx}}{\sqrt{1+sinx}-\sqrt{1-sinx}})` then show that `\frac{dy}{dx}=\pm\frac{1}{2}`

Question No: #132

If `y=\frac{2}{\sqrt{a^2-b^2}}tan^{-1}[\sqrt{\frac{a-b}{a+b}}\tan\frac{x}{2}]` then show that `\frac{dy}{dx}=\frac{1}{a+b\cosx}`
Ans: N.A.
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Question No: #133

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

Question No: #134

Find the derivative of `x^{sin^{-1}x}` w.r.t. `sin^{-1}x`

Question No: #135

Find the derivative of `log_10x` with respect to `tan^{-1}x`

Question No: #136

Find the derivative of `x^2` with respect to `logx`

Question No: #137

Find `\frac{dy}{dx}` where `x=csc^{-1}(\frac{1+t^2}{2t})`, `y=tan^{-1}(\frac{3t-t^3}{1-3t^2})` where `csc` is abbreviation of cosec

Question No: #138

Find `\frac{dy}{dx}`, where `x=sec^{-1}(\frac{1+t^2}{1-t^2})` and `y=tan^{-1}(\frac{3t-t^2}{1-3t^2})`

Question No: #139

Show that the derivative of `sec^{-1}(\frac{1}{2x^2-1})` w.r.t. `\sqrt{1-x^2}` at `x=\frac{1}{2}` is 4

Question No: #140

Find the derivative of `sin^{-1}\frac{2x}{1+x^2}` w.r.t. `tan^{-1}\frac{2x}{1-x^2}` where `x\gt1`