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Popular >

derivative of f(x)=sqrt(x)(x-3)

Solution

derivative of

f (x) = x (x - 3)

Solution

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

Solution steps

\frac{d}{d x} (x (x - 3))

Apply the Product Rule:

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

f = x, g = x - 3

= \frac{d}{d x} (x) (x - 3) + \frac{d}{d x} (x - 3) x

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

\frac{d}{d x} (x - 3) = 1

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

Simplify

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

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

Popular Examples

derivative of (3x-1^4(-2x+9)^5)

\frac{d}{d x} ((3 x - 1)^{4} (- 2 x + 9)^{5})

d/(dp)((400)/(p^2))

\frac{d}{d p} (\frac{400}{p ^{2}})

integral of (9x^2-6x+5)

\int (9 x^{2} - 6 x + 5) d x

derivative of f(x)= x/(x+c/x)derivative of

f (x) = \frac{x}{x + \frac{c}{x}}

y^'=(cos^2(x))(cos^2(2y))

y^{^{'}} = (cos^{2} (x)) (cos^{2} (2 y))

Frequently Asked Questions (FAQ)

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