What is the derivative of ((5x^3+4))/((2x)) ?

The derivative of ((5x^3+4))/((2x)) is (5x^3-2)/(x^2)

What is the first derivative of ((5x^3+4))/((2x)) ?

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

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derivative of

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

\frac{5 x ^{3} - 2}{x ^{2}}

Solution steps

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

Take the constant out:

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

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

\frac{d}{d x} (5 x^{3} + 4) = 15 x^{2}

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

= \frac{1}{2} \cdot \frac{15 x ^{2} x - 1 \cdot ( 5 x ^{3} + 4 )}{x ^{2}}

Simplify

\frac{1}{2} \cdot \frac{15 x ^{2} x - 1 \cdot ( 5 x ^{3} + 4 )}{x ^{2}} : \frac{5 x ^{3} - 2}{x ^{2}}

= \frac{5 x ^{3} - 2}{x ^{2}}

3^{4} x

\frac{cos ( x )}{x ^{2}}

x \cdot e^{x} - 2

23 x - 9

(3 x)^{4 x}

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