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