What is the derivative of (8x^2+6x+2/(sqrt(x))) ?

The derivative of (8x^2+6x+2/(sqrt(x))) is (12x^2+3x-1)/(xsqrt(x))

What is the first derivative of (8x^2+6x+2/(sqrt(x))) ?

The first derivative of (8x^2+6x+2/(sqrt(x))) is (12x^2+3x-1)/(xsqrt(x))

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\frac{d}{d x} (\frac{8 x ^{2} + 6 x + 2}{x})

\frac{12 x ^{2} + 3 x - 1}{x x}

Solution steps

\frac{d}{d x} (\frac{8 x ^{2} + 6 x + 2}{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} + 6 x + 2 ) x - \frac{d}{d x} ( x ) ( 8 x ^{2} + 6 x + 2 )}{( x ) ^{2}}

\frac{d}{d x} (8 x^{2} + 6 x + 2) = 16 x + 6

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

= \frac{( 16 x + 6 ) x - \frac{1}{2 x} ( 8 x ^{2} + 6 x + 2 )}{( x ) ^{2}}

Simplify

\frac{( 16 x + 6 ) x - \frac{1}{2 x} ( 8 x ^{2} + 6 x + 2 )}{( x ) ^{2}} : \frac{12 x ^{2} + 3 x - 1}{x x}

= \frac{12 x ^{2} + 3 x - 1}{x x}

\frac{\partial}{\partial x} (55 x - 0.5 x^{2})

\int \frac{- x - 1}{x ^{2} + 9} d x

\frac{t d y}{d t} + 3 y = t^{4}, t > 0, y (1) = 3

f (x) = x^{3} - 3 x, (2, 2)

\frac{d}{d x} (ln (1 - x^{3}))

What is the derivative of (8x^2+6x+2/(sqrt(x))) ?
The derivative of (8x^2+6x+2/(sqrt(x))) is (12x^2+3x-1)/(xsqrt(x))
What is the first derivative of (8x^2+6x+2/(sqrt(x))) ?
The first derivative of (8x^2+6x+2/(sqrt(x))) is (12x^2+3x-1)/(xsqrt(x))