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# Answer to Question #26703 in Calculus for Michelle Rowlett

Question #26703
Use the chain rule to find the derivative of the function: y=(5x^3+4)^2. y&#039;=?
1
2013-04-08T08:36:40-0400
The chain rule means that if f and g are twodifferentiable functions, then the derivative of their composition

(f(g(x))&#039; = f&#039;(g(x)) * g&#039;(x).
In our case, denote
f(x) = x^2,
g(x) = 5x^3+4Then
y(x) = f(g(x)).

Notice that
f&#039;(x) = (x^2)&#039; =2x
g&#039;(x) = (5x^3+4)&#039;= 15 x^2 whence
y&#039;(x) = f&#039;(g(x)) * g&#039;(x) = 2(5x^3+4) * 15 x^2

Simplifying this expression we get
y&#039;(x) = 2(5x^3+4) * 15 x^2
= (10x^3 + 8)* 15 x^2
= 150x^5 +120x^2For additional practice you can watch our videos on chain rule, you&#039;ll find theoretical explanations and examples showing all the steps.

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