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Popular >

derivative of sqrt(x)(x-2)

Solution

derivative of

x (x - 2)

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = x - 2

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

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

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

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

Simplify

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

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

Graph

Popular Examples

d/(dt)((a+bt+ct^2)/(sqrt(t)))

\frac{d}{d t} (\frac{a + b t + c t ^{2}}{t})

integral of tan^6(3x)

\int tan^{6} (3 x) d x

integral of 2sqrt(3x-1)

\int 2 3 x - 1 d x

5(d^2x)/(dt^2)+4(dx)/(dt)+9x=2cos(3t)

5 \frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 9 x = 2 cos (3 t)

derivative of 7sin(x+7cos(x))

\frac{d}{d x} (7 sin (x) + 7 cos (x))

Frequently Asked Questions (FAQ)

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