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If y = cos (m sin^(-1) x), prove that (1...

If `y = cos (m sin^(-1) x),` prove that `(1-x^2)y_3 -3 xy_2 + ( m^2 -1) y_1=0`

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PREMIERS PUBLISHERS-DIFFEREMTIAL CALCULUS DIFFERENTIABILITY AND METHODS OF DIFFERENTITAION -PROBLEMS FOR PRACTICE
  1. If e^(x)+ e^(y) = e^(x+y), find dy/dx.

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  2. If ax^(2) +2hxy + by^(2) + 2gx + 2fy + c = 0, find dy/dx.

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  3. If y = cos (m sin^(-1) x), prove that (1-x^2)y3 -3 xy2 + ( m^2 -1) y1=...

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  4. Differentiate tan^(-1)(2x/(1 - x^(2))) with respect to cos^(-1)((1 - x...

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  5. If y = sqrt((x-1)(x-2)(x-3)), find dy/dx.

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  6. Differentiate cosec^(-1)((1 + x^(2))/(2x)) with respect to cot^(-1)((1...

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  7. f(x)={(x,0,le,x,le,2),(3x,-,1,2,lt,x,le,3):} then f'(2^(+)) is:

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  8. f(x)={(x,0,le,x,le,1),(2x,-,1,1,lt,x,le,2):} then f'(1^(-)) is :

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  9. If f(x)=x^2 and is differentiable an [1,2] f'(c) at c where c in [1,2]...

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  10. f(x)={(x,0,le,x,le,1),(2x,-,1,1,lt,x,le,2):} then f'(1^(-)) is :

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  11. f(x)=abs(x)+abs(x+1)+abs(x-1)+cosx. At how many points on R, this func...

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  12. f(x)=abs(x)+abs(x-1) find f'(1^(+)):

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  13. f(x)={(2x,-,3,0,le,x,le,2),(x^(2),-,3,2,le,x,le,4):} then f'(2^(+)) an...

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  14. Compute f'(0^(+)) if f(x)=(x(e^(1/x)-1))/(e^(1/x)+1):

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  15. f(x)=ax^(2)+bx+12, f'(2)=11,f'(4)=15, Then a and b are:

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  16. y = tan^(-1)sqrt((1-cosx)/(1+cosx)) dy/dx is:

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  17. y=log(5)x+ 55 then dy/dx is:

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  18. Differentiate (x^(2)-1)/(x^(2)+1) with respect to x:

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  19. y=e^(sinx^(2)), find dy/dx:

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  20. y=e^(sin^(-1)x) find y' at x=0:

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