Given y = f(x) with f(1) = 4 and f'(1) = 3, find(adsbygoogle = window.adsbygoogle || []).push({});

(a) [tex] g'(1) if g(x) = \sqrt {f(x)} [/tex]

(b) [tex] h'(1) if h(x) = f(\sqrt {x}) [/tex]

(a) [tex] g'(x) = \frac {1}{2} f(x)^\frac{-1}{2} * f'(x) [/tex]

[tex] g'(1) = \frac {1}{2} f(1)^\frac{-1}{2} * f'(1) [/tex]

[tex] g'(1) = \frac {1}{2}(4)^\frac{-1}{2} * 3 [/tex]

[tex] g'(1) = \frac {3}{4} [/tex]

(b) [tex] h'(x) = f'(\sqrt{x}) [/tex]

[tex]h'(1) = f'(\sqrt{1}) [/tex]

[tex]h'(1) = f'(1) [/tex]

[tex]h'(1) = 3 [/tex]

Are these correct?

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

Thanks.

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# Homework Help: Given values, find derivatives

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