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y=xe^x show that xdy/dx=(1+x)y...

`y=xe^x `show that `xdy/dx=(1+x)y`

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If y = x^(5) show that x(dy)/(dx)-5y = 0 .

If log(x^2+y^2)=2tan^(-1)(y/x), show that (dy)/(dx)=(x+y)/(x-y)

If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y) ,show that dy/dx=sqrt((1-y^2)/(1-x^2))

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PATHFINDER-DERIVATIVES-QUESTION BANK
  1. If y=secx+tanx then prove that 2(dy/dx)=(1+y^2)

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

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  3. y=xe^x show that xdy/dx=(1+x)y

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  4. Find the diffrential coefficients of y=cosx^0

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  5. If p=at^2+bt+c find [(dp)/dt](t=2) =?

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  6. if 2f(x)+3f(-x)=x^2+x+1 find the value of f'(1)

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  7. If f(9)=9 ,f'(9)=4, underset(xrarr9)"Lt" (sqrt f(x)-3)/(sqrtx-3)=?

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  8. The function f is differentiable at x=a and its derivative be f'(a) sh...

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  9. If y=(x)/(x+2) prove that x(dy)/(dx)=y(1-y)

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  10. show that the function f(x)=abs(x-2)+abs(x-3) is not differentiable at...

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  11. If log(x^2-y^2)/(x^2+Y^2)=a the prove that (dy/dx)=y/x

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  12. prove that d/dx(x^x)=x^x(1+logex)

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  13. y=x^(x^(x^------infty) then prove that dy/dx=(y^2)/(x(1-ylogx))

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  14. If y=tan^(-1)(5ax)/(a^2-6x^2) prove that dy/dx=(3a)/(a^2+9x^2)+(2a)/(a...

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  15. y=sin^(-1)(xsqrt(1-x)+sqrtxsqrt(1-x^2)) show that dy/dx=(1)/(sqrt(1-x^...

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  16. f(x) is differentiable at x=a prove that underset(xrarra)Lt ((x+a)f(a)...

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  17. If y=g{g(x)}, g(0)=0 and g'(0)=2 then find dy/dx at x=0

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  18. 2f(x)+3f(-x)=x^2-x+1 then determine f'(1)

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  19. x=sectheta-costheta , y=sec^n theta- cos^n theta show that (dy/dx)^2=(...

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  20. y=tan^(-1) ((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)) show that dy/d...

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