What is the derivative of (2x^2+4x+2)/(sqrt(x)) ?

The derivative of (2x^2+4x+2)/(sqrt(x)) is (3x^2+2x-1)/(xsqrt(x))

What is the first derivative of (2x^2+4x+2)/(sqrt(x)) ?

The first derivative of (2x^2+4x+2)/(sqrt(x)) is (3x^2+2x-1)/(xsqrt(x))

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derivative of

\frac{2 x ^{2} + 4 x + 2}{x}

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

= \frac{3 x ^{2} + 2 x - 1}{x x}

y = 4 x^{3} - 4 x

\int_{- 1}^{1} \frac{1}{x ^{\frac{1}{3}}} d x

\int_{0}^{\infty} e^{- b t} d t

\int \frac{x ^{2}}{4} - 1 d x

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

What is the derivative of (2x^2+4x+2)/(sqrt(x)) ?
The derivative of (2x^2+4x+2)/(sqrt(x)) is (3x^2+2x-1)/(xsqrt(x))
What is the first derivative of (2x^2+4x+2)/(sqrt(x)) ?
The first derivative of (2x^2+4x+2)/(sqrt(x)) is (3x^2+2x-1)/(xsqrt(x))