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The function f is differentiable at x=a and its derivative be f'(a) show that `underset(xrarra)Lt (xf(a)-af(x))/(x-a)=f(a)-af'(a)`

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f(x) is differentiable at x=a prove that underset(xrarra)Lt ((x+a)f(a)-2af(x))/(x-a)=f(a)-2af'(a)

If a function f(x) is derivable at x = a, then show that underset(x rarr a)lim (x^(2)f(a) - a^(2)f(x))/(2(x-a)) = af(a) - 1/2(a^(2)f'(a))

If the derivatives of f(x) at x=a is f'(a) ,then show that lim_(xrarra)(xf(a)-af(x))/(x-a)=f(a)-af'(a)

If the derivative of f(x) at x = a be f'(a) show that lim_(x to a ) (xf(a)-af(x))/(x-a) = f(a) -af'(a) .

If f(2)=4 ,f'(2)=1 , underset(xrarr2)Lt ((xf(2)-2f(x))/(x-2)) =?

If f(x) is differentiable at x=a then show that lim_(xrarr0)(x^2f(a)-a^2f(x))/(x-a)=2af(a)-a^2f^1(a)

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PATHFINDER-DERIVATIVES-QUESTION BANK
  1. if 2f(x)+3f(-x)=x^2+x+1 find the value of f'(1)

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

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

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

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

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

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

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

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

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

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

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

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  13. 2f(x)+3f(-x)=x^2-x+1 then determine f'(1)

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

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

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  16. f(x)=5x-4 (0ltxle1) =4x^2-3x (1ltxlt2) test whether f(x) is differenti...

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  17. find the derivative of x^x

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  18. Find by the defination the differential coefficient of the following: ...

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  19. Find derivative of the following: sec3x

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  20. Find derivative of the following:e^(sqrtx)

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