If `f(1)=3` , `f'(1)=2` , then `d/(dx)` `{logf(e^x+2x)}` at `x=0` is equal to........

Suppose |(f'(x),f(x)),(f''(x),f'(x))|=0 where f(x) is continuous differentiable function with f'(x) !=0 and satisfies f(0)=1 and f'(0)=2 , then f(x)=e^(lambda x)+k , then lambda+k is equal to ..........

Suppose |(f'(x),f(x)),(f''(x),f'(x))|=0 where f(x) is continuous differentiable function with f'(x) !=0 and satisfies f(0)=1 and f'(0)=2 , then f(x)=e^(lambda x)+k , then lambda+k is equal to ..........

f(x) and g(x) are two differentiable functions on [0, 2] such that f''(x)-g''(x)=0, f'(1)=2, g'(1)=4, f(2)=3 and g(2)=9 , then [f(x)-g(x)] at x=(3)/(2) is equal to -

Let f(x) = (x^2 - x)/(x^2 + 2x) , then d/(dx) (f^(-1)(x))^(-) is equal to

f(x)=(2x-pi)^(3)+2x-cos x,Th e n,(d)/(dx)[f^(-1)(x)] at x=pi is equal to :

If adifferentiabl e function f(x)=e^(x)+2x is given,then equal to (d)/(dx)(f^(-1)(x)) at x=f(ln3) is equal to

If f(x)=tan^(-1)((3x-x^(3))/(1-3x^(2))) then (d)/(dx)(f(x)) is equal to

If (d)/(dx)[f(x)]=(1)/(1+x^(2))," then: "(d)/(dx)[f(x^(3))]=