(x^(5/2)+2x)(x^3-4)

Question

What is the derivative of this function, with ALL work.

Answer 1

Derivative of the function: (x^(5/2)+2x)(x^3-4)

Let y = u*v, where u = (x^(5/2)+2x) and v = (x^3-4)

Then dy/dx = u*v’ + u’*v,

with u’ = du/dx = (5/2)x^(3/2) + 2, and v’ = dv/dx = 3x^2,

giving

dy/dx = ((5/2)x^(3/2) + 2)(3x^2)

Answer: 3((5/2)x^(3/2) + 2).x^2