What is the derivative of (6x^2+3x+7)/(sqrt(x)) ?

The derivative of (6x^2+3x+7)/(sqrt(x)) is (18x^2+3x-7)/(2xsqrt(x))

What is the first derivative of (6x^2+3x+7)/(sqrt(x)) ?

The first derivative of (6x^2+3x+7)/(sqrt(x)) is (18x^2+3x-7)/(2xsqrt(x))

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derivative of

\frac{6 x ^{2} + 3 x + 7}{x}

\frac{18 x ^{2} + 3 x - 7}{2 x x}

Solution steps

\frac{d}{d x} (\frac{6 x ^{2} + 3 x + 7}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 6 x ^{2} + 3 x + 7 ) x - \frac{d}{d x} ( x ) ( 6 x ^{2} + 3 x + 7 )}{( x ) ^{2}}

\frac{d}{d x} (6 x^{2} + 3 x + 7) = 12 x + 3

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

= \frac{( 12 x + 3 ) x - \frac{1}{2 x} ( 6 x ^{2} + 3 x + 7 )}{( x ) ^{2}}

Simplify

\frac{( 12 x + 3 ) x - \frac{1}{2 x} ( 6 x ^{2} + 3 x + 7 )}{( x ) ^{2}} : \frac{18 x ^{2} + 3 x - 7}{2 x x}

= \frac{18 x ^{2} + 3 x - 7}{2 x x}

y^{^{'}} = 0.0011 y \cdot (2900 - y)

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What is the derivative of (6x^2+3x+7)/(sqrt(x)) ?
The derivative of (6x^2+3x+7)/(sqrt(x)) is (18x^2+3x-7)/(2xsqrt(x))
What is the first derivative of (6x^2+3x+7)/(sqrt(x)) ?
The first derivative of (6x^2+3x+7)/(sqrt(x)) is (18x^2+3x-7)/(2xsqrt(x))