What is the derivative of aln(x^2) ?

The derivative of aln(x^2) is (2a)/x

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

The first derivative of aln(x^2) is (2a)/x

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

\frac{2 a}{x}

Solution steps

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

Take the constant out:

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

= a \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

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

Simplify

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

= \frac{2 a}{x}

\int 7 x^{3} d x

f (x) = - 5 x^{2} + x, at x = 3

\int_{0}^{1} (x (x + 1)) d x

- \frac{2}{5 x}

f (x) = 3 x + 6 x, (1, 9)

What is the derivative of aln(x^2) ?
The derivative of aln(x^2) is (2a)/x
What is the first derivative of aln(x^2) ?
The first derivative of aln(x^2) is (2a)/x