Derivative (1st order)

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

Click on each question to see answer & solution.

Question No: #91

If `siny=xsin(a+y)`, then show that `\frac{dy}{dx}=\frac{sin^2(a+y)}{sina}=\frac{sina}{1-2x\cosa+x^2}` where `a\nen\pi`, `n` is an integer.
Ans: N.A.
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Question No: #92

If `f(x)=(\frac{a+x}{b+x})^x+(sinx)^{tanx}` then find the value of `f'(0)`

Question No: #93

If `y=(tanx)^{sinx}` then find the value of `\frac{dy}{dx}` at `x=\frac{\pi}{4}`

Question No: #94

If `y=x^{cosx}+(cosx)^{sinx}` then find the value of `\frac{dy}{dx}`

Question No: #95

If `y=(sinx)^{cosx}+(cosx)^{sinx}` then find the value of `frac{dy}{dx}`

Question No: #96

If `y=(tanx)^{cotx}+(cotx)^{tanx}` then find the value of `\frac{dy}{dx}`
Ans: `(tanx)^{cotx}[csc^2x(1-log\tanx)]+(cotx)^{tanx}[sec^2x(log\cotx-1)]`
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Question No: #97

If `y={(tanx)^{tanx}}^{tanx}`, then find the value of `\frac{dy}{dx}` at `x=\frac{\pi}{4}`
Ans: `2`
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Question No: #98

If `(sinx)^y=x+y` then prove that `\frac{dy}{dx}=\frac{1-(x+y)y\cotx}{(x+y)\ln(sinx)-1}`

Question No: #99

If `x=sec\theta-cos\theta` and `y=sec^n\theta-cos^n\theta`, then show that `(x^2+4)(\frac{dy}{dx})^2=n^2(y^2+4)`
Ans: N.A.
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Question No: #100

If `x=csc\theta-sin\theta`, `y=csc^n\theta-sin^n\theta`, then show that `(x^2+4)(\frac{dy}{dx})^2=n^2(y^2+4)`