What is the derivative of (3x^2-1)/(2xsqrt(x)) ?

The derivative of (3x^2-1)/(2xsqrt(x)) is (3(x^2+1))/(4x^{5/2)}

What is the first derivative of (3x^2-1)/(2xsqrt(x)) ?

The first derivative of (3x^2-1)/(2xsqrt(x)) is (3(x^2+1))/(4x^{5/2)}

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derivative of

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

\frac{3 ( x ^{2} + 1 )}{4 x ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (\frac{3 x ^{2} - 1}{2 x x})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (\frac{3 x ^{2} - 1}{x 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} ( 3 x ^{2} - 1 ) x x - \frac{d}{d x} ( x x ) ( 3 x ^{2} - 1 )}{( x x ) ^{2}}

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

\frac{d}{d x} (x x) = \frac{3 x}{2}

= \frac{1}{2} \cdot \frac{6 xx x - \frac{3 x}{2} ( 3 x ^{2} - 1 )}{( x x ) ^{2}}

Simplify

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

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

\int (2 x)^{3} 2 d x

x \to 2 lim (\frac{1}{4 - x ^{2}})

\int \frac{x ^{4}}{( 2 - x ^{5} ) ^{4}} d x

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

\int e^{2 x} \cdot e^{- x} d x

What is the derivative of (3x^2-1)/(2xsqrt(x)) ?
The derivative of (3x^2-1)/(2xsqrt(x)) is (3(x^2+1))/(4x^{5/2)}
What is the first derivative of (3x^2-1)/(2xsqrt(x)) ?
The first derivative of (3x^2-1)/(2xsqrt(x)) is (3(x^2+1))/(4x^{5/2)}