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

The derivative of (x^2+4/(5x-9)) is (5x^2-18x-20)/((5x-9)^2)

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

The first derivative of (x^2+4/(5x-9)) is (5x^2-18x-20)/((5x-9)^2)

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\frac{d}{d x} (\frac{x ^{2} + 4}{5 x - 9})

\frac{5 x ^{2} - 18 x - 20}{( 5 x - 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 4}{5 x - 9})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 4 ) ( 5 x - 9 ) - \frac{d}{d x} ( 5 x - 9 ) ( x ^{2} + 4 )}{( 5 x - 9 ) ^{2}}

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

\frac{d}{d x} (5 x - 9) = 5

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

Expand

2 x (5 x - 9) - 5 (x^{2} + 4) : 5 x^{2} - 18 x - 20

= \frac{5 x ^{2} - 18 x - 20}{( 5 x - 9 ) ^{2}}

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = - 7.5, y^{^{'}} (0) = \frac{23}{5}

f (x) = 3

x \to 9 - lim (\frac{2}{x - 9})

\int tan^{4} (8 x) d x

\int \frac{1}{v ^{2} + 1} d v

What is the derivative of (x^2+4/(5x-9)) ?
The derivative of (x^2+4/(5x-9)) is (5x^2-18x-20)/((5x-9)^2)
What is the first derivative of (x^2+4/(5x-9)) ?
The first derivative of (x^2+4/(5x-9)) is (5x^2-18x-20)/((5x-9)^2)