What is Dydx of x(x-10)?

Answer 1

Assuming y = x(x - 10)

Either use the product rule:

u = x

v = (x - 10)

→ y = x(x - 10) = uv

d/dx (uv) = v du/dx + u dv/dx

→ dy/dx = d/dx x(x - 10)

= (x - 10)(d/dx x) + (x)(d/dx (x - 10))

= (x - 10)(1) + (x)(1)

= x - 10 + x

= 2x - 10

or expand the brackets and differentiate

dy/dx = d/dx x(x - 10)

= d/dx x² - 10x

= 2x - 10

Answer 2

You can use the product rule for this. But it is probably simpler to open the parentheses first, and then use the rule for the derivative of polynomials.

Answer 3

It is 2x - 10.

Answer 4

It is 2(x - 5).