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if y=x^3 then prove that xdy/dx-3y=0...

if `y=x^3` then prove that `xdy/dx-3y=0`

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  • APPLICATION OF DERIVATIVES

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PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. Given, f(x)=(x-1)/(2x^2-7x+5) when xne1 Find the derivative of f(x) a...

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  2. lf y=sqrt((1-x)/(1+x)) find dy/dxand prove that (1-x^2)(dy)/(dx)+y=0

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  3. if y=x^3 then prove that xdy/dx-3y=0

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  4. Find the intervals in which the following functions are increasing or ...

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  5. Find the intervals in which the follwing functions are increasing or d...

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  6. Find the intervals in which the follwing functions are increasing or d...

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  7. Find lim(x->0)(sin(pisin^2(x))/x^2)

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  8. lim(x to 0) (1-cosx)/x^2 = ?

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  9. If f(x)=ax^3+bx^2+cx+d has local extrema at two points of opposite si...

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  10. Prove that if 2a0^2lt15a all roots of x^5-a0x^4+3ax^3+bx^2+cx+d=0 can...

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  11. Let a,b,c be real. If ax^2+bx+c=0 has two real roots alpha,beta where ...

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  12. Let a+b=4, where a gt 2 and let g(x)be a differentiable function. If ...

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  13. On the curve x^3=12y the abscissa changes at a faster rate than the or...

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  14. A spherical iron ball 10 cm in radius is coated with a layer of ice of...

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  15. The function f(x)=tan^(-1)x-x decreases in the interval

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  16. The function f(x)=2log(x-2)-x^2+4x+1 increases in the interval

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  17. The function f(x)=sin^4x+cos^4x increasing if :

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  18. The length of the longest interval in which the function 3sinx-4sin^3x...

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  19. The function f(x) =tan^(-1)(sinx+cosx) is an increasing function in

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  20. The function f defined by f(x)=4x^4-2x+1 is increasing for

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