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Today I was learning with the wolframalpha problem generator and I got the following exercise

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Is this a mistake? How did they get to this solution?

Magdiragdag
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Maik Klein
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1 Answers1

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In order to differentiate this function, let us first get it into a more amicable form: $f(x) = (6x+3)^{\frac{1}{3}}$. Notice that this is composite function. If we call $g(x) = 6x+3$ and $h(x) = x^{\frac{1}{3}}$, then $f(x) = h(g(x))$. Let us now examine that which we must do in order to differentiate our function $f$. $f(x)=h(g(x))$. Therefore, $f^{'}(x) = ((h(g(x))))^{'} = h^{'}(g(x))*g^{'}(x)$. This differentiation comes from the chain rule. Therefore, in taking the derivative of $f(x) = (6x+3)^{\frac{1}{3}}$, we obtain $\frac{1}{3}(6x+3)^{-\frac{2}{3}}*6 = 2(6x+3)^{-\frac{2}{3}} = f^{'}(x)$.

What is to be taken from this problem is this: never forget your power-rule or chain rule.

Hope this helped.

wxm5539
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