Differentiate the function.g(x) = x^2(1 − 5x)

Answer 1

g(x) = x^2(1 − 5x)

To differentiate this, you have 2 options:

1. Expand the right hand side to get: g(x) = x^2 - 5x^3, then take the derivative: g' = 2x - 15x^2
2. Use the product rule : If you have u*v, the derivative is uv' + vu':

u = x^2 u' = 2x

v = 1 - 5x, v' = -5

g'(x) = x^2 * (-5) + 2x * (1-5x)

-5x^2 + 2x - 10x^2

g' = 2x - 15x^2