What is the derivative of 460(1+x/(x^2+80)) ?

The derivative of 460(1+x/(x^2+80)) is (460(-x^2+80))/((x^2+80)^2)

What is the first derivative of 460(1+x/(x^2+80)) ?

The first derivative of 460(1+x/(x^2+80)) is (460(-x^2+80))/((x^2+80)^2)

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\frac{d}{d x} (460 (1 + \frac{x}{x ^{2} + 80}))

\frac{460 ( - x ^{2} + 80 )}{( x ^{2} + 80 ) ^{2}}

Solution steps

\frac{d}{d x} (460 (1 + \frac{x}{x ^{2} + 80}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 460 \frac{d}{d x} (1 + \frac{x}{x ^{2} + 80})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 460 (\frac{d}{d x} (1) + \frac{d}{d x} (\frac{x}{x ^{2} + 80}))

\frac{d}{d x} (1) = 0

\frac{d}{d x} (\frac{x}{x ^{2} + 80}) = \frac{- x ^{2} + 80}{( x ^{2} + 80 ) ^{2}}

= 460 (0 + \frac{- x ^{2} + 80}{( x ^{2} + 80 ) ^{2}})

Simplify

460 (0 + \frac{- x ^{2} + 80}{( x ^{2} + 80 ) ^{2}}) : \frac{460 ( - x ^{2} + 80 )}{( x ^{2} + 80 ) ^{2}}

= \frac{460 ( - x ^{2} + 80 )}{( x ^{2} + 80 ) ^{2}}

\int \frac{5 x - 2}{( x - 2 ) ^{2}} d x

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

\frac{d}{d x} (\frac{1}{27} (9 x^{2} + 6)^{\frac{3}{2}})

y^{^{'}} + 9 y = t + e^{- 5 t}

(x - y) d x + x d y = 0

What is the derivative of 460(1+x/(x^2+80)) ?
The derivative of 460(1+x/(x^2+80)) is (460(-x^2+80))/((x^2+80)^2)
What is the first derivative of 460(1+x/(x^2+80)) ?
The first derivative of 460(1+x/(x^2+80)) is (460(-x^2+80))/((x^2+80)^2)