Calculating value of a derivative

[Needhelp123]

I was wondering if someone could help me make sense of what this problem is asking. "Given that f(x) is a differentiable function and f'(4)=3, find the value of d/dx f(sqrtx) when x=4". I know that the derivative of sqrtx =1/(2sqrtx) and if I substitute 4 into the equation, I get 1/4. I know I'm missing something, but can't see what it is!

Any help would be greatly appreciated!

 

[Quaid]

I was wondering if someone could help me make sense of what this problem is asking. "Given that f(x) is a differentiable function and f'(4)=3, find the value of d/dx f(sqrtx) when x=4".

I know that the derivative of sqrtx =1/(2sqrtx) and if I substitute 4 into the equation, I get 1/4. I know I'm missing something, but can't see what it is!

Hi there:

You're missing that f(√x) is function notation for a composite function.

That is, consider g(x) = √x

Now your exercise is to calculate d/dx f(g(x)) instead of d/dx √x

Chain rule!

Cheers :cool:

 

[Needhelp123]

Hi there:

You're missing that f(√x) is function notation for a composite function.

That is, consider g(x) = √x

Now your exercise is to calculate d/dx f(g(x)) instead of d/dx √x

Chain rule!

Cheers :cool:

Thanks so much! I knew it was something simple I just wasn't seeing! Much appreciated!