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Popular >

derivative of sqrt(x)(x-10)

Solution

derivative of

x (x - 10)

Solution

\frac{3 x - 10}{2 x}

Solution steps

\frac{d}{d x} (x (x - 10))

Apply the Product Rule:

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

f = x, g = x - 10

= \frac{d}{d x} (x) (x - 10) + \frac{d}{d x} (x - 10) x

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

\frac{d}{d x} (x - 10) = 1

= \frac{1}{2 x} (x - 10) + 1 \cdot x

Simplify

\frac{1}{2 x} (x - 10) + 1 \cdot x : \frac{3 x - 10}{2 x}

= \frac{3 x - 10}{2 x}

Popular Examples

derivative of (2x^2/(3x-1))

\frac{d}{d x} (\frac{2 x ^{2}}{3 x - 1})

integral of (sqrt(x)+3)^3

\int (x + 3)^{3} d x

limit as x approaches-4 of x^3+4x^2-8x

x \to - 4 lim (x^{3} + 4 x^{2} - 8 x)

yln(y)dx+(x-ln(y))dy=0

y ln (y) d x + (x - ln (y)) d y = 0

(\partial)/(\partial x)(x^3y+e^{xy^2})

\frac{\partial}{\partial x} (x^{3} y + e^{x y^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)(x-10) ?
The derivative of sqrt(x)(x-10) is (3x-10)/(2sqrt(x))
What is the first derivative of sqrt(x)(x-10) ?
The first derivative of sqrt(x)(x-10) is (3x-10)/(2sqrt(x))