Derivative (2nd order)

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

Click on each question to see answer & solution.

Question No: #11

If `y=e^{\frac{1}{x}}`, then find `\frac{d^2y}{dx^2}`

Question No: #12

If `F(x)=f(x)\cdot\phi(x)` and `f'(x)\cdot\phi\'(x)=a` where `a` constant, then prove that `\frac{F''}{F}=\frac{f''}{f}+\frac{\phi\''}{\phi}+\frac{2a}{f\phi}`

Question No: #13

If `x=f(t)` and `y=g(t)` then show that `\frac{d^2y}{dx^2}=\frac{x_1y_2-y_1x_2}{x_1^3}`

Question No: #14

If `x\sin\theta+y\cos\theta=a` and `x\cos\theta-y\sin\theta=b`, then show that value of `\frac{dx}{d\theta}\cdot\frac{d^2y}{d\theta^2}-\frac{d^2x}{d\theta^2}\cdot\frac{dy}{d\theta}` is constant.
Ans: N.A.
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Question No: #15

If `x=t^2+2t`, `y=t^3-3t` then show that `\frac{d^2y}{dx^2}=\frac{3}{4(t+1)}`

Question No: #16

If `x=cost`, `y=logt` then show that `\frac{d^2y}{dx^2}+(\frac{dy}{dx})^2=0` at `t=\frac{\pi}{2}`

Question No: #17

If `x=a\cos\2t`, `y=a\sin\2t` then find the value of `\frac{d^2y}{dx^2}` in form of `t`

Question No: #18

If `x=sint`, `y=sin\kt` then show that `(1-x^2)\frac{d^2y}{dx^2}-x\frac{dy}{dx}+k^2y=0` where `k` is a constant
Ans: N.A.
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Question No: #19

If `x=tant` and `y=tanpt`, then show that `(1+x^2)\frac{d^2y}{dx^2}+2(x-py)\frac{dy}{dx}=0`

Question No: #20

If `x=e^tsint` and `y=e^tcost` then show that `(x+y)^2\frac{d^2y}{dx^2}=2(x\frac{dy}{dx}-y)`
Ans: N.A.
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