What is the derivative of sqrt(x)(x-8) ?

The derivative of sqrt(x)(x-8) is (3x-8)/(2sqrt(x))

What is the first derivative of sqrt(x)(x-8) ?

The first derivative of sqrt(x)(x-8) is (3x-8)/(2sqrt(x))

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derivative of

x (x - 8)

\frac{3 x - 8}{2 x}

Solution steps

\frac{d}{d x} (x (x - 8))

Apply the Product Rule:

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

f = x, g = x - 8

= \frac{d}{d x} (x) (x - 8) + \frac{d}{d x} (x - 8) x

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

\frac{d}{d x} (x - 8) = 1

= \frac{1}{2 x} (x - 8) + 1 \cdot x

Simplify

\frac{1}{2 x} (x - 8) + 1 \cdot x : \frac{3 x - 8}{2 x}

= \frac{3 x - 8}{2 x}

f (x) = 2 x^{3} - x^{2} + 2, at x = 2

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

\frac{d}{d x} (\frac{1}{14} (e^{7 x} + e^{- 7 x}))

\int_{0}^{1} π (tan (\frac{π}{4} y))^{2} d y

\frac{\partial}{\partial x} (\frac{5 x + 4 y}{3 x + 2 y})

What is the derivative of sqrt(x)(x-8) ?
The derivative of sqrt(x)(x-8) is (3x-8)/(2sqrt(x))
What is the first derivative of sqrt(x)(x-8) ?
The first derivative of sqrt(x)(x-8) is (3x-8)/(2sqrt(x))