What is the derivative of 500q-(q^2)/(ln(q+300)) ?

The derivative of 500q-(q^2)/(ln(q+300)) is 500-(2qln(q+300)(q+300)-q^2)/(ln^2(q+300)(q+300))

What is the first derivative of 500q-(q^2)/(ln(q+300)) ?

The first derivative of 500q-(q^2)/(ln(q+300)) is 500-(2qln(q+300)(q+300)-q^2)/(ln^2(q+300)(q+300))

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derivative of

500 q - \frac{q ^{2}}{ln ( q + 300 )}

500 - \frac{2 q ln ( q + 300 ) ( q + 300 ) - q ^{2}}{ln ^{2} ( q + 300 ) ( q + 300 )}

Solution steps

\frac{d}{d q} (500 q - \frac{q ^{2}}{ln ( q + 300 )})

Apply the Sum/Difference Rule:

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

= \frac{d}{d q} (500 q) - \frac{d}{d q} (\frac{q ^{2}}{ln ( q + 300 )})

\frac{d}{d q} (500 q) = 500

\frac{d}{d q} (\frac{q ^{2}}{ln ( q + 300 )}) = \frac{2 q ln ( q + 300 ) ( q + 300 ) - q ^{2}}{ln ^{2} ( q + 300 ) ( q + 300 )}

= 500 - \frac{2 q ln ( q + 300 ) ( q + 300 ) - q ^{2}}{ln ^{2} ( q + 300 ) ( q + 300 )}

(x + 2 y) d x + x d y = 0

x \to - 2 lim (1 + \frac{2}{x + 2})

\frac{d y}{d t} = 0.17 y + 200

\int_{0}^{1} \frac{y}{e ^{6 y}} d y

y^{^{'}} = e^{4 y} (sin (5 x))

What is the derivative of 500q-(q^2)/(ln(q+300)) ?
The derivative of 500q-(q^2)/(ln(q+300)) is 500-(2qln(q+300)(q+300)-q^2)/(ln^2(q+300)(q+300))
What is the first derivative of 500q-(q^2)/(ln(q+300)) ?
The first derivative of 500q-(q^2)/(ln(q+300)) is 500-(2qln(q+300)(q+300)-q^2)/(ln^2(q+300)(q+300))