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

The derivative of (3ax^2+x/(2x)) is (3a)/2

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

The first derivative of (3ax^2+x/(2x)) is (3a)/2

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

\frac{3 a}{2}

Solution steps

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

Take the constant out:

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

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

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

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

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

Simplify

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

= \frac{3 a}{2}

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