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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (8 x^{2})

3 y^{^{''}} - 5 y^{^{'}} - 2 y = x^{3} - 2 x

x \to - 2 lim (x^{3} - 2 x^{2} + 1)

\frac{d}{d x} (arctan (x - 5))

\frac{d}{d x} (\frac{( 3 x ^{5} - 7 x ^{2} - 4 )}{x ^{2}})

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