What is the derivative of (8x^2+8x+4/(sqrt(x))) ?

The derivative of (8x^2+8x+4/(sqrt(x))) is (12x^2+4x-2)/(xsqrt(x))

What is the first derivative of (8x^2+8x+4/(sqrt(x))) ?

The first derivative of (8x^2+8x+4/(sqrt(x))) is (12x^2+4x-2)/(xsqrt(x))

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\frac{d}{d x} (\frac{8 x ^{2} + 8 x + 4}{x})

\frac{12 x ^{2} + 4 x - 2}{x x}

Solution steps

\frac{d}{d x} (\frac{8 x ^{2} + 8 x + 4}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 x ^{2} + 8 x + 4 ) x - \frac{d}{d x} ( x ) ( 8 x ^{2} + 8 x + 4 )}{( x ) ^{2}}

\frac{d}{d x} (8 x^{2} + 8 x + 4) = 16 x + 8

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

= \frac{( 16 x + 8 ) x - \frac{1}{2 x} ( 8 x ^{2} + 8 x + 4 )}{( x ) ^{2}}

Simplify

\frac{( 16 x + 8 ) x - \frac{1}{2 x} ( 8 x ^{2} + 8 x + 4 )}{( x ) ^{2}} : \frac{12 x ^{2} + 4 x - 2}{x x}

= \frac{12 x ^{2} + 4 x - 2}{x x}

\frac{\partial}{\partial x} (x + 2 y)

\int \frac{5 x + 4}{( x + 8 ) ^{2} ( x - 1 )} d x

\frac{s ^{2} + 9}{s ( s + 4 )}

\frac{d y}{d x} = \frac{x - 1}{x + 3} \frac{y - 2}{y - 3}

\frac{2 s + 3}{s ^{2} + 6 s + 13}

What is the derivative of (8x^2+8x+4/(sqrt(x))) ?
The derivative of (8x^2+8x+4/(sqrt(x))) is (12x^2+4x-2)/(xsqrt(x))
What is the first derivative of (8x^2+8x+4/(sqrt(x))) ?
The first derivative of (8x^2+8x+4/(sqrt(x))) is (12x^2+4x-2)/(xsqrt(x))