What is the derivative of 500(1+(4x/(50+x^2))) ?

The derivative of 500(1+(4x/(50+x^2))) is (2000(-x^2+50))/((x^2+50)^2)

What is the first derivative of 500(1+(4x/(50+x^2))) ?

The first derivative of 500(1+(4x/(50+x^2))) is (2000(-x^2+50))/((x^2+50)^2)

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\frac{d}{d x} (500 (1 + \frac{4 x}{50 + x ^{2}}))

\frac{2000 ( - x ^{2} + 50 )}{( x ^{2} + 50 ) ^{2}}

Solution steps

\frac{d}{d x} (500 (1 + \frac{4 x}{50 + x ^{2}}))

Take the constant out:

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

= 500 \frac{d}{d x} (1 + \frac{4 x}{50 + x ^{2}})

Apply the Sum/Difference Rule:

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

= 500 (\frac{d}{d x} (1) + \frac{d}{d x} (\frac{4 x}{50 + x ^{2}}))

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

\frac{d}{d x} (\frac{4 x}{50 + x ^{2}}) = \frac{4 ( 50 - x ^{2} )}{( 50 + x ^{2} ) ^{2}}

= 500 (0 + \frac{4 ( 50 - x ^{2} )}{( 50 + x ^{2} ) ^{2}})

Simplify

500 (0 + \frac{4 ( 50 - x ^{2} )}{( 50 + x ^{2} ) ^{2}}) : \frac{2000 ( - x ^{2} + 50 )}{( x ^{2} + 50 ) ^{2}}

= \frac{2000 ( - x ^{2} + 50 )}{( x ^{2} + 50 ) ^{2}}

\int z^{'} d z

\int \frac{x ^{2}}{x ^{2} - 49} d x

(2 x + 3) + (2 y - 2) \frac{d y}{d x} = 0

3 x^{2} + 2 x y + 3 y^{2} + (x^{2} + 6 x y) y^{^{'}} = 0

\frac{d}{d x} (4 x^{4} e^{- x})

What is the derivative of 500(1+(4x/(50+x^2))) ?
The derivative of 500(1+(4x/(50+x^2))) is (2000(-x^2+50))/((x^2+50)^2)
What is the first derivative of 500(1+(4x/(50+x^2))) ?
The first derivative of 500(1+(4x/(50+x^2))) is (2000(-x^2+50))/((x^2+50)^2)