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Popular >

derivative of 6ln(x^2)

Solution

\frac{d}{d x} (6 ln (x^{2}))

Solution

\frac{12}{x}

Solution steps

\frac{d}{d x} (6 ln (x^{2}))

Take the constant out:

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

= 6 \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

= 6 \cdot \frac{1}{x ^{2}} \cdot 2 x

Simplify

6 \cdot \frac{1}{x ^{2}} \cdot 2 x : \frac{12}{x}

= \frac{12}{x}

Popular Examples

integral of x*tan^2(x)

\int x \cdot tan^{2} (x) d x

limit as x approaches 0 of sqrt(3x+1)

x \to 0 lim (3 x + 1)

(y^'-e^{-t}+3)/y =-3

\frac{y ^{^{'}} - e ^{- t} + 3}{y} = - 3

limit as n approaches infinity of \sum_{i=1}^n(1+(2i)/n)^3(2/n)

n \to \infty lim (i = 1 \sum n (1 + \frac{2 i}{n})^{3} (\frac{2}{n}))

derivative of (x^3+x-2/(x-x^2))

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

Frequently Asked Questions (FAQ)

What is the derivative of 6ln(x^2) ?
The derivative of 6ln(x^2) is (12)/x
What is the first derivative of 6ln(x^2) ?
The first derivative of 6ln(x^2) is (12)/x