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Popular >

derivative of sqrt(x)(x-4)

Solution

derivative of

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

sum from n=6 to infinity of e^{5-6n}

n = 6 \sum \infty e^{5 - 6 n}

derivative of ln((sqrt(4+x^2)/x))

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

derivative of f(t)=sqrt(t)-1/(sqrt(t))derivative of

f (t) = t - \frac{1}{t}

integral of (24)/((1-x^2)^{3/2)}

\int \frac{24}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

y^{''}-y^'=x^2-3x

y^{^{''}} - y^{^{'}} = x^{2} - 3 x

Frequently Asked Questions (FAQ)

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