What is the ((x-sqrt(x))*(x+sqrt(x)))^' ?

The ((x-sqrt(x))*(x+sqrt(x)))^' is 2x-1

What is the first ((x-sqrt(x))*(x+sqrt(x)))^' ?

The first ((x-sqrt(x))*(x+sqrt(x)))^' is 2x-1

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((x - x) \cdot (x + x))^{^{'}}

2 x - 1

Solution steps

((x - x) (x + x))^{'}

Apply the Product Rule:

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

f = x - x, g = x + x

= (x - x)^{^{'}} (x + x) + (x + x)^{^{'}} (x - x)

(x - x)^{'} = 1 - \frac{1}{2 x}

(x + x)^{'} = 1 + \frac{1}{2 x}

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

Simplify

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

= 2 x - 1

What is the ((x-sqrt(x))*(x+sqrt(x)))^' ?
The ((x-sqrt(x))*(x+sqrt(x)))^' is 2x-1
What is the first ((x-sqrt(x))*(x+sqrt(x)))^' ?
The first ((x-sqrt(x))*(x+sqrt(x)))^' is 2x-1