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

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

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

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

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derivative of

\frac{ln ( x ^{2} )}{x}

\frac{2 - ln ( x ^{2} )}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

= \frac{\frac{2}{x} x - 1 \cdot ln ( x ^{2} )}{x ^{2}}

Simplify

\frac{\frac{2}{x} x - 1 \cdot ln ( x ^{2} )}{x ^{2}} : \frac{2 - ln ( x ^{2} )}{x ^{2}}

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

sin (x^{l}) o gx + x^{\frac{1}{2}} w

sin^{5} (x) + 4

1 - x^{4} e^{- 8 x}

y = x^{4} - 3 x^{- 2} + 1

1 7^{x - 1}

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