What is the derivative of (8+5x)/(x^2+9) ?

The derivative of (8+5x)/(x^2+9) is (-5x^2-16x+45)/((x^2+9)^2)

What is the first derivative of (8+5x)/(x^2+9) ?

The first derivative of (8+5x)/(x^2+9) is (-5x^2-16x+45)/((x^2+9)^2)

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derivative of

\frac{8 + 5 x}{x ^{2} + 9}

\frac{- 5 x ^{2} - 16 x + 45}{( x ^{2} + 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 + 5 x}{x ^{2} + 9})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 + 5 x ) ( x ^{2} + 9 ) - \frac{d}{d x} ( x ^{2} + 9 ) ( 8 + 5 x )}{( x ^{2} + 9 ) ^{2}}

\frac{d}{d x} (8 + 5 x) = 5

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

= \frac{5 ( x ^{2} + 9 ) - 2 x ( 8 + 5 x )}{( x ^{2} + 9 ) ^{2}}

Expand

5 (x^{2} + 9) - 2 x (8 + 5 x) : - 5 x^{2} - 16 x + 45

= \frac{- 5 x ^{2} - 16 x + 45}{( x ^{2} + 9 ) ^{2}}

\int_{0}^{\frac{π}{2}} 9 cos^{5} (x) d x

\int e^{2 x} x + \frac{3}{2} e^{2 x} d x

n = 1 \sum \infty \frac{3 n}{5 n + 1}

2 x, 2 x - 4, 0, 4

\int - 2 t^{2} d t

What is the derivative of (8+5x)/(x^2+9) ?
The derivative of (8+5x)/(x^2+9) is (-5x^2-16x+45)/((x^2+9)^2)
What is the first derivative of (8+5x)/(x^2+9) ?
The first derivative of (8+5x)/(x^2+9) is (-5x^2-16x+45)/((x^2+9)^2)