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Popular >

derivative of (x-sqrt(x))(x+sqrt(x))

Solution

derivative of

(x - x) (x + x)

Solution

2 x - 1

Solution steps

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

Apply the Product Rule:

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

f = x - x, g = x + x

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

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

\frac{d}{d 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

Popular Examples

limit as x approaches 0 of (1-3/x)^x

x \to 0 lim ((1 - \frac{3}{x})^{x})

integral of 1/(r^2)

\int \frac{1}{r ^{2}} d r

(\partial)/(\partial x)((sin(x))^2)

\frac{\partial}{\partial x} ((sin (x))^{2})

integral from-1 to 1 of (x-x^3)

\int_{- 1}^{1} (x - x^{3}) d x

(\partial)/(\partial x)(te^{(-x^2)/(2t)})

\frac{\partial}{\partial x} (t e^{\frac{- x ^{2}}{2 t}})

Frequently Asked Questions (FAQ)

What is the derivative of (x-sqrt(x))(x+sqrt(x)) ?
The derivative of (x-sqrt(x))(x+sqrt(x)) is 2x-1
What is the first derivative of (x-sqrt(x))(x+sqrt(x)) ?
The first derivative of (x-sqrt(x))(x+sqrt(x)) is 2x-1