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

The derivative of (x^2+4/(4x^3-5x)) is (-4x^4-53x^2+20)/((4x^3-5x)^2)

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

The first derivative of (x^2+4/(4x^3-5x)) is (-4x^4-53x^2+20)/((4x^3-5x)^2)

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

\frac{- 4 x ^{4} - 53 x ^{2} + 20}{( 4 x ^{3} - 5 x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (4 x^{3} - 5 x) = 12 x^{2} - 5

= \frac{2 x ( 4 x ^{3} - 5 x ) - ( 12 x ^{2} - 5 ) ( x ^{2} + 4 )}{( 4 x ^{3} - 5 x ) ^{2}}

Expand

2 x (4 x^{3} - 5 x) - (12 x^{2} - 5) (x^{2} + 4) : - 4 x^{4} - 53 x^{2} + 20

= \frac{- 4 x ^{4} - 53 x ^{2} + 20}{( 4 x ^{3} - 5 x ) ^{2}}

- 5 e^{- 5 x + 2}

\int \frac{e ^{x}}{e ^{x} + e} d x

\int \frac{1}{y} d y

\frac{1}{2 x + 1}

\int_{- π}^{2 π} π cos^{2} (x) d x

What is the derivative of (x^2+4/(4x^3-5x)) ?
The derivative of (x^2+4/(4x^3-5x)) is (-4x^4-53x^2+20)/((4x^3-5x)^2)
What is the first derivative of (x^2+4/(4x^3-5x)) ?
The first derivative of (x^2+4/(4x^3-5x)) is (-4x^4-53x^2+20)/((4x^3-5x)^2)