Derivative (1st order)

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

Click on each question to see answer & solution.

Question No: #1

If `y=sinx°` then find `\frac{dy}{dx}`

Question No: #2

Find the value of `\frac{d}{dx}(x^x)`
Ans: `x^x(1+logx)`
SEE SOLUTION

Question No: #3

Find the value of `frac{d}{dx}5^{f(x)}`

Question No: #4

If `f(x)` is an even function and `f'(0)` exists, then find the value of `f'(0)`
Ans: `0`
SEE SOLUTION

Question No: #5

If `y=\sqrt{2x}-\sqrt{2/x}+frac{x+4}{4-x}`, then find `(\frac{dy}{dx})_{x=2}`
Ans: `2\3/4`
SEE SOLUTION

Question No: #6

If `y=\sqrt{sin\sqrt{x}}` then find `\frac{dy}{dx}`
Ans: `frac{1}{4\sqrt{x}}\frac{cos\sqrt{x}}{\sqrt{sin\sqrt{x}}}`
SEE SOLUTION

Question No: #7

Find the value of `\frac{d}{dx}{cos(logx)}`
Ans: `-\frac{\sin(logx)}{x}`
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Question No: #8

If `u=e^{ax}\sinbx` and `v=e^{ax}\cosbx`, then show that `(\frac{du}{dx})^2+(\frac{dv}{dx})^2=(a^2+b^2)e^{2ax}`

Question No: #9

If `x=\sqrt{t}+\frac{1}{\sqrt{t}}`, then find the value of `2t\frac{dx}{dt}+x`
Ans: `2\sqrt{t}`
SEE SOLUTION

Question No: #10

If `\sqrt{x}+\sqrt{y}=4` then find the value of `\frac{dy}{dx}` at `x=1`
Ans: `-3`
SEE SOLUTION