What is the derivative of (6x^2+4x+4/(sqrt(x))) ?

The derivative of (6x^2+4x+4/(sqrt(x))) is (9x^2+2x-2)/(xsqrt(x))

What is the first derivative of (6x^2+4x+4/(sqrt(x))) ?

The first derivative of (6x^2+4x+4/(sqrt(x))) is (9x^2+2x-2)/(xsqrt(x))

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\frac{d}{d x} (\frac{6 x ^{2} + 4 x + 4}{x})

\frac{9 x ^{2} + 2 x - 2}{x x}

Solution steps

\frac{d}{d x} (\frac{6 x ^{2} + 4 x + 4}{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} + 4 x + 4 ) x - \frac{d}{d x} ( x ) ( 6 x ^{2} + 4 x + 4 )}{( x ) ^{2}}

\frac{d}{d x} (6 x^{2} + 4 x + 4) = 12 x + 4

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

= \frac{( 12 x + 4 ) x - \frac{1}{2 x} ( 6 x ^{2} + 4 x + 4 )}{( x ) ^{2}}

Simplify

\frac{( 12 x + 4 ) x - \frac{1}{2 x} ( 6 x ^{2} + 4 x + 4 )}{( x ) ^{2}} : \frac{9 x ^{2} + 2 x - 2}{x x}

= \frac{9 x ^{2} + 2 x - 2}{x x}

x \to \frac{π}{2} lim (sec (x))

x \to 0 + lim (ln (x) \cdot tan (x))

x \frac{d y}{d x} + 2 y = 2 e^{x}

\frac{5}{π s ^{2}}

2 x - 3

What is the derivative of (6x^2+4x+4/(sqrt(x))) ?
The derivative of (6x^2+4x+4/(sqrt(x))) is (9x^2+2x-2)/(xsqrt(x))
What is the first derivative of (6x^2+4x+4/(sqrt(x))) ?
The first derivative of (6x^2+4x+4/(sqrt(x))) is (9x^2+2x-2)/(xsqrt(x))