What is the derivative of ln(((2x+9^3)/(x^2))) ?

The derivative of ln(((2x+9^3)/(x^2))) is (2(x-9))/(x(2x+9))

What is the first derivative of ln(((2x+9^3)/(x^2))) ?

The first derivative of ln(((2x+9^3)/(x^2))) is (2(x-9))/(x(2x+9))

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\frac{d}{d x} (ln (\frac{( 2 x + 9 ) ^{3}}{x ^{2}}))

\frac{2 ( x - 9 )}{x ( 2 x + 9 )}

Solution steps

\frac{d}{d x} (ln (\frac{( 2 x + 9 ) ^{3}}{x ^{2}}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{( 2 x + 9 ) ^{3}}{x ^{2}}) = \frac{2 ( 2 x + 9 ) ^{2} ( x - 9 )}{x ^{3}}

= \frac{1}{\frac{( 2 x + 9 ) ^{3}}{x ^{2}}} \cdot \frac{2 ( 2 x + 9 ) ^{2} ( x - 9 )}{x ^{3}}

Simplify

\frac{1}{\frac{( 2 x + 9 ) ^{3}}{x ^{2}}} \cdot \frac{2 ( 2 x + 9 ) ^{2} ( x - 9 )}{x ^{3}} : \frac{2 ( x - 9 )}{x ( 2 x + 9 )}

= \frac{2 ( x - 9 )}{x ( 2 x + 9 )}

What is the derivative of ln(((2x+9^3)/(x^2))) ?
The derivative of ln(((2x+9^3)/(x^2))) is (2(x-9))/(x(2x+9))
What is the first derivative of ln(((2x+9^3)/(x^2))) ?
The first derivative of ln(((2x+9^3)/(x^2))) is (2(x-9))/(x(2x+9))