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Popular >

derivative of (x^2-5x/(sqrt(x)))

Solution

\frac{d}{d x} (\frac{x ^{2} - 5 x}{x})

Solution

\frac{3 x - 5}{2 x}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 5 x}{x})

Simplify

\frac{x ^{2} - 5 x}{x} : x (x - 5)

= \frac{d}{d x} (x (x - 5))

Apply the Product Rule:

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

f = x, g = x - 5

= \frac{d}{d x} (x) (x - 5) + \frac{d}{d x} (x - 5) x

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

\frac{d}{d x} (x - 5) = 1

= \frac{1}{2 x} (x - 5) + 1 \cdot x

Simplify

\frac{1}{2 x} (x - 5) + 1 \cdot x : \frac{3 x - 5}{2 x}

= \frac{3 x - 5}{2 x}

Popular Examples

integral of 1/(sqrt(121-x^2))

\int \frac{1}{121 - x ^{2}} d x

derivative of (x^2+1/(x+4))

\frac{d}{d x} (\frac{x ^{2} + 1}{x + 4})

7x^2y^{''}+15xy^'+y=0

7 x^{2} y^{^{''}} + 15 x y^{^{'}} + y = 0

(x^3-6x^2+2x-2)^'

(x^{3} - 6 x^{2} + 2 x - 2)^{^{'}}

derivative of sin(x)+1/2 cot(x)derivative of

sin (x) + \frac{1}{2} cot (x)

Frequently Asked Questions (FAQ)

What is the derivative of (x^2-5x/(sqrt(x))) ?
The derivative of (x^2-5x/(sqrt(x))) is (3x-5)/(2sqrt(x))
What is the first derivative of (x^2-5x/(sqrt(x))) ?
The first derivative of (x^2-5x/(sqrt(x))) is (3x-5)/(2sqrt(x))