Derivative (1st order)

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

Click on each question to see answer & solution.

Question No: #21

If `y=x^{e^x}` then find `\frac{dy}{dx}`
Ans: `x^{e^x}\cdot\e^x(1/x+logx)`
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Question No: #22

If `x^y=e^{x-y}`, then show that `\frac{dy}{dx}=\frac{logx}{(logex)^2}`
Ans: N.A.
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Question No: #23

If `y^x=e^{y-x}` then show that `\frac{dy}{dx}=\frac{(log\ey)^2}{logy}`
Ans: N.A.
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Question No: #24

If `y=log_10x`, then find the value of `\frac{dy}{dx}`

Question No: #25

Find the value of `\frac{d}{dx}{log_7(log_7\x)}`
Ans: `frac{log_7e}{x\ logx}`
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Question No: #26

If `f(x)=log_ex`, then find the derivative of `f(log_ex)` with respect to `x`
Ans: `\frac{1}{x\log_ex}`
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Question No: #27

If `y=10^{10^x}` then find the value of `\frac{dy}{dx}`
Ans: `10^{10^x}10^x(log_e10)^2`
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Question No: #28

If `y=log|x|` then find the value of `\frac{dy}{dx}`
Ans: `1/x`
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Question No: #29

If `f(x)=log\sin(\sqrt{x^2+1})`, then find `f'(x)`.
Ans: `cot(\sqrt{x^2+1}) \cdot \frac{x}{\sqrt{x^2+1}}`
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Question No: #30

If `f(x)=log(tan\frac{x}{2})` then find `f\'(x)`
Ans: `csc x`
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