(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If y=f((x^{2}+9)^{0.5}) and f'(5)=-2, find dy/dx when x=4

2. Relevant equations

chain rule: dy/dx=(dy/du)(du/dx)

3. The attempt at a solution

In my opinion giving f'(5)=-2 is unnecessary as:

y=f(u)=u, u=(x^{2}+9)^{0.5}

dy/dx= (dy/du)(du/dx)

(dy/du)= 1

(du/dx)= x/((x^{2}+9))^{0.5}

dy/dx = (1)(x/((x^{2}+9))^{0.5})

= x/((x^{2}+9))^{0.5}

dy/dx(4) = 4/(16+9)^{0.5}

= 4/(25)^{0.5}

= 4/5

the answer is -8/5

I would appreciate help very much.

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# Homework Help: Chain rule with leibniz notation

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