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

The derivative of (2x^2+8x+6/(sqrt(x))) is (3x^2+4x-3)/(xsqrt(x))

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

The first derivative of (2x^2+8x+6/(sqrt(x))) is (3x^2+4x-3)/(xsqrt(x))

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Popular >

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

\frac{3 x ^{2} + 4 x - 3}{x x}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{3 x ^{2} + 4 x - 3}{x x}

\int_{3}^{\infty} e^{- \frac{x}{4}} d x

\frac{\partial}{\partial x} (9 cos (y e^{x y}) sin (x))

\int \frac{6 x ^{2} + x + 3}{( x ^{2} + 2 ) ( x - 9 )} d x

\frac{\partial}{\partial y} (\frac{1}{x})

(1, 1), (8, - \frac{3}{4})

What is the derivative of (2x^2+8x+6/(sqrt(x))) ?
The derivative of (2x^2+8x+6/(sqrt(x))) is (3x^2+4x-3)/(xsqrt(x))
What is the first derivative of (2x^2+8x+6/(sqrt(x))) ?
The first derivative of (2x^2+8x+6/(sqrt(x))) is (3x^2+4x-3)/(xsqrt(x))