Derivative (1st order)

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

Click on each question to see answer & solution.

Question No: #51

If `y\cdot\e^y=x` then show that `\frac{dy}{dx}=\frac{y}{x(1+y)}`
Ans: N.A.
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Question No: #52

If `y=e^{\frac{y}{x}}`, then show that `\frac{dy}{dx}=\frac{y^2}{x(y-x)}`
Ans: N.A.
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Question No: #53

If `f(x)=sin(logx)` and `y=f(\frac{2x+3}{3-2x})`, then find `\frac{dy}{dx}`.

Question No: #54

Find the derivative of $\frac{5x}{\sqrt[3]{1-x^2}}+sin^2(2x-3)$ w.r.t. `x`
Ans: `\frac{5(3-x^2)}{(1-x^2)^{4/3}}+2sin(4x-6)`
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Question No: #55

Find the derivative w.r.t. `x` of following, `y=log_sinx secx + 10^{x^2}`

Question No: #56

If `y=log_{sinx}secx+10^{x^2}`, then find `\frac{dy}{dx}`
Ans: `\frac{tanx\log(sinx)-cotx\log(secx)}{{log(sinx)}^2}+2x10^{x^2}log_e10`
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Question No: #57

If `siny+e^{-x\cosy}=e` then the value of `\frac{dy}{dx}` at `(1,\pi)`

Question No: #58

If `y=x^{n-1}logx`, then find the value of `x\frac{dy}{dx}+(1-n)y`

Question No: #59

If `y=\frac{x}{\sqrt{1+x^2}}`, then prove that `x^3\frac{dy}{dx}=y^3`
Ans: N.A.
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Question No: #60

If `y=\sqrt{1+\sqrt{1+x^4}}`, then prove that `y(y^2-1)\frac{dy}{dx}=x^3`