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

The derivative of (3x^2+1)/(2x) is (3x^2-1)/(2x^2)

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

The first derivative of (3x^2+1)/(2x) is (3x^2-1)/(2x^2)

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

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

\frac{d x}{d x} = 1

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

Simplify

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

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

\int cos (x) lo g_{10} (2) 2^{x} d x

\frac{d}{d x} (x sin (y - z))

\int \frac{42}{1 - cos ( 7 x )} d x

f (x) = 15 x^{3} - 10 x^{2} + 1, (1, 6)

\int_{b}^{1} 5 ln (x) d x

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