homework 3.6 the chain rule\nscore: 10/100 answered: 1/10\nquestion 2\ntextbook videos +\nuse the chain rule…
homework 3.6 the chain rule\nscore: 10/100 answered: 1/10\nquestion 2\ntextbook videos +\nuse the chain rule to find the derivative of\n f(x)=2(-4x^{6}+6x^{4})^{13} \nyou do not need to expand out your answer.\n f(x)=\nquestion help: video\nsubmit question jump to answer
Answer
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:
$26(-4x^{6}+6x^{4})^{12}(-24x^{5}+24x^{3})$