B) H(u) = (u - √u)(2u^2+1) = (u - u^.5)(2u^2+1)
H' = (u - u^.5)(4 u) + (2u^2+1) (1 - .5 u^-.5)
etc, now you do the first one
Find the derivative of each of the following functions using the product rule. you do not have to simplify your answer.
A) f(y) = (1/y^2 - 3/y^4)(y+5y^3)
B) H(u) = (u - √u)(2u^2+1)
3 answers
Can you explain me how you got .5 and 4u. I'm so lost.
I write √x as x^(1/2) or x^.5
then we know the derivative of x^n is n x(n-1)
so the derivative of x^.5 is .5 x^(.5-1) = .5 x^-.5 [ which by the way is .5/x^(1/2) ]
same way for x^2
derivative is 2 x^(2-1) = 2 x^ 1 = 2 x
so for 2 u^2 it is 2 * 2 u = 4 u
then we know the derivative of x^n is n x(n-1)
so the derivative of x^.5 is .5 x^(.5-1) = .5 x^-.5 [ which by the way is .5/x^(1/2) ]
same way for x^2
derivative is 2 x^(2-1) = 2 x^ 1 = 2 x
so for 2 u^2 it is 2 * 2 u = 4 u