Derivative (1st order)

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

Click on each question to see answer & solution.

Question No: #11

If `x^{\frac{3}{2}}+y^{\frac{3}{2}}=a^{\frac{3}{2}}`, then show that `\frac{dy}{dx}+\sqrt{\frac{x}{y}}=0`
Ans: N.A.
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Question No: #12

If `y=e^{sin^{-1}x}` and `z=e^{-cos^{-1}x}` then find the value of `\frac{dy}{dz}`
Ans: `e^{\frac{\pi}{2}}`
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Question No: #13

If `x=\sqrt{a^{sin^{-1}t}}`, `y=\sqrt{a^{cos^{-1}t}}` then show that `\frac{dy}{dx}=-\frac{y}{x}`
Ans: N.A.
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Question No: #14

If `f(x)=(x+1)^x+x^{x+1}`, then find the value of `f'(1)`
Ans: `3 + 2 log 2`
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Question No: #15

If `y=(logx)^x+x^{logx}`, then find `\frac{dy}{dx}`

Question No: #16

If `f(x)=(sinx)^x+x^x` then find `f'(x)`
Ans: `x^x(1+logx)+(sinx)^x(x\cotx+log\sinx)`
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Question No: #17

If `y=\frac{3x-2}{2x+1}` where `(x\ne\frac{1}{2})`, then justify the statement `\frac{dy}{dx}=1\div(\frac{dx}{dy})`
Ans: N.A.
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Question No: #18

If `f(x)=|1-2x|` then find the value of `f'(2)`

Question No: #19

If `f(x)=x\|x|`, then show that `f'(x)=2|x|`
Ans: N.A.
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Question No: #20

If `f(x)=|x|^3`, then find `f'(0)`
Ans: `0`
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