What is the d/(du)((u-sqrt(u))(u+sqrt(u))) ?

The d/(du)((u-sqrt(u))(u+sqrt(u))) is 2u-1

What is the first d/(du)((u-sqrt(u))(u+sqrt(u))) ?

The first d/(du)((u-sqrt(u))(u+sqrt(u))) is 2u-1

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\frac{d}{d u} ((u - u) (u + u))

2 u - 1

Solution steps

\frac{d}{d u} ((u - u) (u + u))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = u - u, g = u + u

= \frac{d}{d u} (u - u) (u + u) + \frac{d}{d u} (u + u) (u - u)

\frac{d}{d u} (u - u) = 1 - \frac{1}{2 u}

\frac{d}{d u} (u + u) = 1 + \frac{1}{2 u}

= (1 - \frac{1}{2 u}) (u + u) + (1 + \frac{1}{2 u}) (u - u)

Simplify

(1 - \frac{1}{2 u}) (u + u) + (1 + \frac{1}{2 u}) (u - u) : 2 u - 1

= 2 u - 1

\frac{\partial}{\partial x} (\frac{1}{1 - \frac{x}{a} - \frac{y}{b}})

\int \frac{1}{12} x d x

sin (0.5 x)

y^{^{'}} = x + 8 y

\frac{d y}{d t} - y = 1, y (0) = 1

What is the d/(du)((u-sqrt(u))(u+sqrt(u))) ?
The d/(du)((u-sqrt(u))(u+sqrt(u))) is 2u-1
What is the first d/(du)((u-sqrt(u))(u+sqrt(u))) ?
The first d/(du)((u-sqrt(u))(u+sqrt(u))) is 2u-1