What is the derivative of f(x)=(6x^2-1)/(2sqrt(x)) ?

The derivative of f(x)=(6x^2-1)/(2sqrt(x)) is (18x^2+1)/(4xsqrt(x))

What is the first derivative of f(x)=(6x^2-1)/(2sqrt(x)) ?

The first derivative of f(x)=(6x^2-1)/(2sqrt(x)) is (18x^2+1)/(4xsqrt(x))

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derivative of

f (x) = \frac{6 x ^{2} - 1}{2 x}

\frac{18 x ^{2} + 1}{4 x x}

Solution steps

\frac{d}{d x} (\frac{6 x ^{2} - 1}{2 x})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (\frac{6 x ^{2} - 1}{x})

Apply the Quotient Rule:

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

= \frac{1}{2} \cdot \frac{\frac{d}{d x} ( 6 x ^{2} - 1 ) x - \frac{d}{d x} ( x ) ( 6 x ^{2} - 1 )}{( x ) ^{2}}

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

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

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

Simplify

\frac{1}{2} \cdot \frac{12 x x - \frac{1}{2 x} ( 6 x ^{2} - 1 )}{( x ) ^{2}} : \frac{18 x ^{2} + 1}{4 x x}

= \frac{18 x ^{2} + 1}{4 x x}

What is the derivative of f(x)=(6x^2-1)/(2sqrt(x)) ?
The derivative of f(x)=(6x^2-1)/(2sqrt(x)) is (18x^2+1)/(4xsqrt(x))
What is the first derivative of f(x)=(6x^2-1)/(2sqrt(x)) ?
The first derivative of f(x)=(6x^2-1)/(2sqrt(x)) is (18x^2+1)/(4xsqrt(x))