0
$\begingroup$

Use the chain rule to find $dy/dx$ for $y= [3x^2-13]^3$

Any help would be greatly appreciated!

Edit: I have function $\frac{d}{dx}[f(g(x))] = f'(g(x))g'(x)$, not sure how to create a composition of functions from the given expression.

  • 3
    I 'll help you help yourself. Write down the chain rule in your question, and try to understand where you can apply it. Can you create a composition of functions, from the given expression? – 2017-01-19
  • 2
    "*not sure how to create a composition of functions*..." Brackets are usually a good way to organize your thoughts... do you see any brackets or parenthesis in the original? $y=[\dots]^3$ should look like something – 2017-01-19
  • 0
    Should g(x)=3x^2 - 13? – 2017-01-19
  • 0
    @Czar That's a great start. Now, can you figure out $f$? – 2017-01-19
  • 0
    Would this be x^3? – 2017-01-19

1 Answers 1

1

Hint. Your function is given by $y(x) = f(g(x))$ with $$f(x) = x^3, \quad\quad\text{and}\quad\quad g(x) = 3x^2-13.$$ Now apply the chain rule.

  • 0
    Thank you for clarifying the values. I came to conclude those values, thus plugging into f'(g(x))g'(x) would render 18x(3x^2-13)^2 – 2017-01-19
  • 0
    You are completely correct. – 2017-01-19