Question

homework 3.6 the chain rule
score: 10/100 answered: 1/10
question 2
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use the chain rule to find the derivative of
f(x)=2(-4x^{6}+6x^{4})^{13}
you do not need to expand out your answer.
f(x)=
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Explanation:

Step1: Identify outer - inner functions

Let $u=-4x^{6}+6x^{4}$, then $y = 2u^{13}$.

Step2: Differentiate outer function

The derivative of $y$ with respect to $u$ is $\frac{dy}{du}=2\times13u^{12}=26u^{12}$.

Step3: Differentiate inner function

The derivative of $u$ with respect to $x$ is $\frac{du}{dx}=-4\times6x^{5}+6\times4x^{3}=-24x^{5}+24x^{3}$.

Step4: Apply chain - rule

By the chain - rule $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$, substitute $u=-4x^{6}+6x^{4}$ back in. So $f^{\prime}(x)=26(-4x^{6}+6x^{4})^{12}\cdot(-24x^{5}+24x^{3})$.

Answer:

$26(-4x^{6}+6x^{4})^{12}(-24x^{5}+24x^{3})$