Given values, find derivatives

[Jacobpm64]

Given y = f(x) with f(1) = 4 and f'(1) = 3, find

(a) $$g'(1) if g(x) = \sqrt {f(x)}$$
(b) $$h'(1) if h(x) = f(\sqrt {x})$$

(a) $$g'(x) = \frac {1}{2} f(x)^\frac{-1}{2} * f'(x)$$
$$g'(1) = \frac {1}{2} f(1)^\frac{-1}{2} * f'(1)$$
$$g'(1) = \frac {1}{2}(4)^\frac{-1}{2} * 3$$
$$g'(1) = \frac {3}{4}$$

(b) $$h'(x) = f'(\sqrt{x})$$
$$h'(1) = f'(\sqrt{1})$$
$$h'(1) = f'(1)$$
$$h'(1) = 3$$

Are these correct?

I'm not sure if this was the correct approach.

Thanks.

 

[courtrigrad]

(a) correct(b) If $$h(x) = f(\sqrt{x})$$, then $$h'(x) = f'(\sqrt{x})\frac{1}{2}x^{-\frac{1}{2}}$$. So it should be $$\frac{3}{2}$$

 

[Jacobpm64]

thanks, just a simple mistake