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dsp73
4 years ago
13

Find the value of the given function's derivative at x=3

Mathematics
1 answer:
Rasek [7]4 years ago
7 0
<h2>Explanation:</h2>

According to the chain rule, if we have a function:

f(x)=k(g(x))

The derivative at a point a will be:

f'(a)=k'(g(a))g'(a)

We know that:

f'(3)=k'(g(3))g'(3)\\ \\ \\ a=3 \\ \\ \\ Then: \\ \\ g(3)=2(3)-3^2 \\ \\ g(3)=6-9 \\ \\ g(3)=-3 \\ \\ \\ k'(g(3))=k'(-3)=2 \\ \\ \\ g'(x)=2-2x \\ \\ g'(3)=2-2(3)=-4 \\ \\ \\ Finally: \\ \\ f'(3)=2(-4) \\ \\ \boxed{f'(3)=-8}

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