Chain Rule (HSC SSCE Mathematics Advanced): Quizzes

Differentiating composite functions

One function's output used as another's input

$u = 4x^3 - 2x + 7$

What operation is performed last?

$\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$

$\frac{d}{dx}([f(x)]^n) = n[f(x)]^{n-1} \times f'(x)$

Bring down power, reduce by 1, multiply by $f'(x)$

Substitute back to express answer in $x$

Convert them to index form

Yes, it works for fractional exponents