What is the derivative of 1/2 ln(x^2) ?

The derivative of 1/2 ln(x^2) is 1/x

What is the first derivative of 1/2 ln(x^2) ?

The first derivative of 1/2 ln(x^2) is 1/x

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\frac{d}{d x} (\frac{1}{2} ln (x^{2}))

\frac{1}{x}

Solution steps

\frac{d}{d x} (\frac{1}{2} ln (x^{2}))

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{x ^{2}} \frac{d}{d x} (x^{2})

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

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

= \frac{1}{2} \cdot \frac{1}{x ^{2}} \cdot 2 x

Simplify

\frac{1}{2} \cdot \frac{1}{x ^{2}} \cdot 2 x : \frac{1}{x}

= \frac{1}{x}

\int \frac{1}{sin ( x ) - cos ( x )} d x

f (x) = 2 x (x^{2} - 4 x + 5)^{6}, at x = 2

\frac{d}{d X} (X^{2})

\int_{1}^{3} x^{4} (ln (x))^{2} d x

8 e^{- 2 x}

What is the derivative of 1/2 ln(x^2) ?
The derivative of 1/2 ln(x^2) is 1/x
What is the first derivative of 1/2 ln(x^2) ?
The first derivative of 1/2 ln(x^2) is 1/x