Find the derivative

Question

Find the derivative of the equation. y=(2x⁴-5e^{-x^2})(cubic root(x²-4x+4))

Answer 1

Use the product rule:

For f(x) = u•v, then f '(x) = u'v + uv'

where u = 2x⁴ - 5e^(-x²) which means u' = 8x³ + 10xe^(-x²)

and v = cuberoot(x² - 4x + 4) or (x² - 4x + 4)^(1/3) meaning v' = ((2x - 4)/3)(x² - 4x + 4)^(-2/3)

Note that each of these requires use of the chain rule.

Put these together (using f '(x) = u'v + uv') to find the derivative