Derivative (2nd order)

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

Click on each question to see answer & solution.

Question No: #31

If `x^2+y^2=a^2` then show that `\frac{(1+y_1^2)^\frac{3}{2}}{y_2}=-a` where `a` is constant and `y_1`, `y_2` are first & second order derivative
Ans: N.A.
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Question No: #32

If `y^{\frac{1}{3}}+y^{-\frac{1}{3}}=2x`, then prove that `(x^2-1)\frac{d^2y}{dx^2}+x\frac{dy}{dx}=9y`
Ans: N.A.
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Question No: #33

If `2x=y^{frac{1}{m}}+y^{-\frac{1}{m}}`, then show that `(x^2-1)y_2+xy_1=m^2y`
Ans: N.A.
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Question No: #34

If `(a+bx)e^{\frac{x}{y}}=x`, then show that `x^3\frac{d^2y}{dx^2}=(x\frac{dy}{dx}-y)^2`

Question No: #35

If `y=\frac{1}{1+x+x^2+x^3}` then find the value of `[\frac{dy}{dx}]_{x=0}` and `[\frac{d^2y}{dx^2}]_{x=0}`

Question No: #36

If `ax^2+2hxy+by^2=1`, then show that `\frac{d^2y}{dx^2}=\frac{h^2-ab}{(hx+by)^3}`

Question No: #37

If `x\sqrt{1+y}+y\sqrt{1+x}=0`, then show that `(1+x)\frac{d^2y}{dx^2}+2\frac{dy}{dx}=0` and `\frac{d^2y}{dx^2}=\frac{2}{(1+x)^3}`
Ans: N.A.
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Question No: #38

If `\sqrt{y+x}+\sqrt{y-x}=c` (`c` is a non-zero constant), then show that `\frac{d^2y}{dx^2}=\frac{2}{c^2}`

Question No: #39

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

Question No: #40

If `y=(x+\sqrt{x^2-1})^m` then show that `(1-x^2)y_2-xy_1+m^2y=0`
Ans: N.A.
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