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Popular >

derivative of y=sqrt(x)(x-4)

Solution

derivative of

y = x (x - 4)

Solution

\frac{3 x - 4}{2 x}

Solution steps

\frac{d}{d x} (x (x - 4))

Apply the Product Rule:

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

f = x, g = x - 4

= \frac{d}{d x} (x) (x - 4) + \frac{d}{d x} (x - 4) x

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

\frac{d}{d x} (x - 4) = 1

= \frac{1}{2 x} (x - 4) + 1 \cdot x

Simplify

\frac{1}{2 x} (x - 4) + 1 \cdot x : \frac{3 x - 4}{2 x}

= \frac{3 x - 4}{2 x}

Popular Examples

integral of-1/2 cos(2x)(2x)

\int - \frac{1}{2} cos (2 x) (2 x) d x

derivative of (x+3/(7x^2e^x))

\frac{d}{d x} (\frac{x + 3}{7 x ^{2} e ^{x}})

derivative of 16cos(x)

\frac{d}{d x} (16 cos (x))

integral of pi*x^2

\int π \cdot x^{2} d x

integral of 1/(sqrt(3x+2))

\int \frac{1}{3 x + 2} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=sqrt(x)(x-4) ?
The derivative of y=sqrt(x)(x-4) is (3x-4)/(2sqrt(x))
What is the first derivative of y=sqrt(x)(x-4) ?
The first derivative of y=sqrt(x)(x-4) is (3x-4)/(2sqrt(x))