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

The derivative of 500x-(x^2/(ln(x+300))) is 500-(2xln(x+300)(x+300)-x^2)/(ln^2(x+300)(x+300))

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

The first derivative of 500x-(x^2/(ln(x+300))) is 500-(2xln(x+300)(x+300)-x^2)/(ln^2(x+300)(x+300))

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{d}{d x} ((3 x^{2} - 6 x + 10) (x^{3}))

y^{^{''}} + 2 y^{^{'}} + 5 y = e^{(- x)} sec (2 x)

4 e^{5 x}

\frac{d}{d x} (e^{\frac{x}{y}} ln (\frac{x ^{2}}{y}))

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