What is the derivative of (7-2x/(x^2+8)) ?

The derivative of (7-2x/(x^2+8)) is (2x^2-14x-16)/((x^2+8)^2)

What is the first derivative of (7-2x/(x^2+8)) ?

The first derivative of (7-2x/(x^2+8)) is (2x^2-14x-16)/((x^2+8)^2)

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\frac{d}{d x} (\frac{7 - 2 x}{x ^{2} + 8})

\frac{2 x ^{2} - 14 x - 16}{( x ^{2} + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{7 - 2 x}{x ^{2} + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 7 - 2 x ) ( x ^{2} + 8 ) - \frac{d}{d x} ( x ^{2} + 8 ) ( 7 - 2 x )}{( x ^{2} + 8 ) ^{2}}

\frac{d}{d x} (7 - 2 x) = - 2

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

= \frac{( - 2 ) ( x ^{2} + 8 ) - 2 x ( 7 - 2 x )}{( x ^{2} + 8 ) ^{2}}

Simplify

\frac{( - 2 ) ( x ^{2} + 8 ) - 2 x ( 7 - 2 x )}{( x ^{2} + 8 ) ^{2}} : \frac{2 x ^{2} - 14 x - 16}{( x ^{2} + 8 ) ^{2}}

= \frac{2 x ^{2} - 14 x - 16}{( x ^{2} + 8 ) ^{2}}

y = 1.25 x, x = 8.5 - y^{2}

\frac{d}{d x} (48 x (4 x^{2} + 9)^{5})

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

\int \frac{x ^{2} + 4 x - 5}{x ^{3} - 1} d x

f (x) = 1680 (2 x + 5)^{4}

What is the derivative of (7-2x/(x^2+8)) ?
The derivative of (7-2x/(x^2+8)) is (2x^2-14x-16)/((x^2+8)^2)
What is the first derivative of (7-2x/(x^2+8)) ?
The first derivative of (7-2x/(x^2+8)) is (2x^2-14x-16)/((x^2+8)^2)