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If x=phi (t), y=psi(t), then (d ^(2)y)/(...

If `x=phi (t), y=psi(t),` then `(d ^(2)y)/(dx ^(2))=`

A

`(phi'Psi''-Psi'phi'')/((phi)^(2))`

B

`(phi'Psi''-Psi'phi'')/((phi')^(3))`

C

`(phi'')/(Psi'')`

D

`(Psi'')/(phi'')`

Text Solution

Verified by Experts

The correct Answer is:
B
We have, `x=phi(t),y=Psi(t).`
`:." "(dy)/(dx)=((dy)/(dt))/((dx)/(dt))=(Psi')/(phi')`
`implies" "(d^(2)y)/(dx^(2))=(d)/(dx)((Psi')/(phi'))=(d)/(dt)((Psi')/(phi'))(dt)/(dx)`
`implies" "(d^(2)y)/(dx^(2))=(phi'Psi''-Psi'phi'')/(phi'2)xx(1)/(phi')=(phi'Psi''-Psi'phi'')/(phi'3)`
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OBJECTIVE RD SHARMA ENGLISH-DIFFERENTIATION-Chapter Test
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  3. If e^y+xy=e then the value of (d^2y)/(dx^2) for x=0 is

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  4. If sqrt(x+y) +sqrt(y-x)=5, then (d^(2)y)/(dx ^(2))=

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  5. "If "ax^(2)+2hxy+by^(2)=1," then "(d^(2)y)/(dx^(2)) is

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  6. If f(x)=sin{(pi)/(2)[x]-x^(5)},1ltxlt2 and [.] denotes the greatest in...

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  7. f(x) is a polynomial of degree

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  8. If y=sin(log(e)x), then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx) is equal to

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  9. If f(x)=(1-x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+...

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  10. "If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).

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  11. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

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  12. If y=sin^(-1){(5x+12 sqrt(1-x^(2)))/(13)}, find (dy)/(dx).

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  13. If f(x)=cos^(-1){(1-(log(e)x)^(2))/(1+(log(e)x)^(2))}, then f'( e )

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  14. y=sin^(-1)[sqrt(x-ax)-sqrt(a-ax)]

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  15. Let f(x)=(x^3+2)^(30) If f^n (x) is a polynomial of degree 20 where f^...

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  17. If f(x)=10cosx+(13+2x)sinx then f''(x)+f(x)=

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  18. Let a function f:RtoR satisfy the equation f(x+y)=f(x)=f(Y)AAx, yepsil...

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  19. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

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  20. If f'(x)=arc tan((x^(x)-x^(-x))/(2)), then f'(1) is equal to

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  21. Let f(x)=2^(2x-1)" and "g(x)=-2^(x)+2xlog2. Then the set of points sat...

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