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

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

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

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

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derivative of

f (x) = \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}}

h \to 0 lim (3 - 4 h)

\frac{d}{d x} (- 600 x^{- 2})

x, x, 0, 2

\int \frac{1}{5 x + 1} d x

\int e^{2 x} - 1 d x

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