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

The derivative of (8x^2+9)/(x^2+5) is (62x)/((x^2+5)^2)

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

The first derivative of (8x^2+9)/(x^2+5) is (62x)/((x^2+5)^2)

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derivative of

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

\frac{62 x}{( x ^{2} + 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (8 x^{2} + 9) = 16 x

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

= \frac{16 x ( x ^{2} + 5 ) - 2 x ( 8 x ^{2} + 9 )}{( x ^{2} + 5 ) ^{2}}

Expand

16 x (x^{2} + 5) - 2 x (8 x^{2} + 9) : 62 x

= \frac{62 x}{( x ^{2} + 5 ) ^{2}}

45

\frac{3}{x ^{9}}

y^{^{'}} = 7 x + y, y (0) = 9

\int 3 x^{2} - 12 d x

\int x^{9} x^{5} + 2 d x

What is the derivative of (8x^2+9)/(x^2+5) ?
The derivative of (8x^2+9)/(x^2+5) is (62x)/((x^2+5)^2)
What is the first derivative of (8x^2+9)/(x^2+5) ?
The first derivative of (8x^2+9)/(x^2+5) is (62x)/((x^2+5)^2)