derivative y=(4x^2+6x+2)/(sqrt(x))

Solução

derivada de

y = \frac{4 x ^{2} + 6 x + 2}{x}

\frac{6 x ^{2} + 3 x - 1}{x x}

Passos da solução

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

Aplicar a regra do quociente:

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

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

\frac{d}{d x} (4 x^{2} + 6 x + 2) = 8 x + 6

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

= \frac{( 8 x + 6 ) x - \frac{1}{2 x} ( 4 x ^{2} + 6 x + 2 )}{( x ) ^{2}}

Simplificar

\frac{( 8 x + 6 ) x - \frac{1}{2 x} ( 4 x ^{2} + 6 x + 2 )}{( x ) ^{2}} : \frac{6 x ^{2} + 3 x - 1}{x x}

= \frac{6 x ^{2} + 3 x - 1}{x x}

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