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Popular >

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

Solution

derivative of

f (x) = 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

y^{''}+2y^'+y=10e^{-t}

y^{^{''}} + 2 y^{^{'}} + y = 10 e^{- t}

derivative of-2xe^{-2x}

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

integral of (x^2+x-1)/(x^3+2x^2+x)

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

integral of 1/(sqrt(x^2+y^2))

\int \frac{1}{x ^{2} + y ^{2}} d x

inverse oflaplace 9/(s^2+9s+9)*1/s inverse laplace

\frac{9}{s ^{2} + 9 s + 9} \cdot \frac{1}{s}

Frequently Asked Questions (FAQ)

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