What is the derivative of (4x^2+8x+6/(sqrt(x))) ?

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

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

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

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

\frac{6 x ^{2} + 4 x - 3}{x x}

Solution steps

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

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

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

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

Simplify

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

= \frac{6 x ^{2} + 4 x - 3}{x x}

\int_{0}^{1} x 4 + 9 x^{2} d x

\int e^{2 x} \cdot sin (e^{x}) d x

\frac{\partial}{\partial x} (\frac{5 x yz}{x ^{2} + y ^{2} + z ^{2}})

y^{^{'}} + 2 y = 10 sin (t)

f (x) = 3 x^{2} + 5

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