Differentiation

Question

y= -x⁵(1 - x)

 

I have to use the product rule to answer this question. 

 

The answer is 6x⁵ - 5x⁴

 

Can someone explain this to me and show how to solve it?

 

Thank you so much!

Answer 1

Product Rule:  If y = f(x)g(x), then dy/dx = f'(x)g(x) + g'(x)f(x)

 

So, if y = -x⁵(1-x), f(x) = -x⁵, and g(x) = 1-x, then:

 

  dy/dx = -5x⁴(1-x) + (-1)(-x⁵)

 

           = -5x⁴ + 5x⁵ + x⁵ = 6x⁵ - 5x⁴

 

By the way, an easier way to do the problem is to multiply out the original function to get f(x) = -x⁵ + x⁶ and then differentiate.