What is the derivative of (3x^2-4x+5/(6sqrt(x))) ?

The derivative of (3x^2-4x+5/(6sqrt(x))) is (9x^2-4x-5)/(12xsqrt(x))

What is the first derivative of (3x^2-4x+5/(6sqrt(x))) ?

The first derivative of (3x^2-4x+5/(6sqrt(x))) is (9x^2-4x-5)/(12xsqrt(x))

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\frac{d}{d x} (\frac{3 x ^{2} - 4 x + 5}{6 x})

\frac{9 x ^{2} - 4 x - 5}{12 x x}

Solution steps

\frac{d}{d x} (\frac{3 x ^{2} - 4 x + 5}{6 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{6} \frac{d}{d x} (\frac{3 x ^{2} - 4 x + 5}{x})

Apply the Quotient Rule:

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

= \frac{1}{6} \cdot \frac{\frac{d}{d x} ( 3 x ^{2} - 4 x + 5 ) x - \frac{d}{d x} ( x ) ( 3 x ^{2} - 4 x + 5 )}{( x ) ^{2}}

\frac{d}{d x} (3 x^{2} - 4 x + 5) = 6 x - 4

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

= \frac{1}{6} \cdot \frac{( 6 x - 4 ) x - \frac{1}{2 x} ( 3 x ^{2} - 4 x + 5 )}{( x ) ^{2}}

Simplify

\frac{1}{6} \cdot \frac{( 6 x - 4 ) x - \frac{1}{2 x} ( 3 x ^{2} - 4 x + 5 )}{( x ) ^{2}} : \frac{9 x ^{2} - 4 x - 5}{12 x x}

= \frac{9 x ^{2} - 4 x - 5}{12 x x}

x \frac{d y}{d x} + y = 9 x y^{2}

x \to 2 + lim (\frac{1}{( x - 2 ) ^{2}})

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 81})

y^{^{'}} - 2 y = 3 x^{2}

x \to 4 lim (x^{2} - 16)

What is the derivative of (3x^2-4x+5/(6sqrt(x))) ?
The derivative of (3x^2-4x+5/(6sqrt(x))) is (9x^2-4x-5)/(12xsqrt(x))
What is the first derivative of (3x^2-4x+5/(6sqrt(x))) ?
The first derivative of (3x^2-4x+5/(6sqrt(x))) is (9x^2-4x-5)/(12xsqrt(x))