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

The derivative of ((2x+3))/((x^3-5)) is (-4x^3-9x^2-10)/((x^3-5)^2)

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

The first derivative of ((2x+3))/((x^3-5)) is (-4x^3-9x^2-10)/((x^3-5)^2)

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derivative of

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

\frac{- 4 x ^{3} - 9 x ^{2} - 10}{( x ^{3} - 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Expand

2 (x^{3} - 5) - 3 x^{2} (2 x + 3) : - 4 x^{3} - 9 x^{2} - 10

= \frac{- 4 x ^{3} - 9 x ^{2} - 10}{( x ^{3} - 5 ) ^{2}}

4 cos (4 x^{2})

\frac{d}{d t} (\frac{( sin ( t ) )}{( 1 - cos ( t ) )})

e^{3} x

(x^{2} + 1) e^{x}

\frac{d}{d t} (- 2 + 5 t)

What is the derivative of ((2x+3))/((x^3-5)) ?
The derivative of ((2x+3))/((x^3-5)) is (-4x^3-9x^2-10)/((x^3-5)^2)
What is the first derivative of ((2x+3))/((x^3-5)) ?
The first derivative of ((2x+3))/((x^3-5)) is (-4x^3-9x^2-10)/((x^3-5)^2)