What is the derivative of ln(x^{12}) ?

The derivative of ln(x^{12}) is (12)/x

What is the first derivative of ln(x^{12}) ?

The first derivative of ln(x^{12}) is (12)/x

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\frac{d}{d x} (ln (x^{12}))

\frac{12}{x}

Solution steps

\frac{d}{d x} (ln (x^{12}))

Apply the chain rule:

\frac{1}{x ^{12}} \frac{d}{d x} (x^{12})

= \frac{1}{x ^{12}} \frac{d}{d x} (x^{12})

\frac{d}{d x} (x^{12}) = 12 x^{11}

= \frac{1}{x ^{12}} \cdot 12 x^{11}

Simplify

\frac{1}{x ^{12}} \cdot 12 x^{11} : \frac{12}{x}

= \frac{12}{x}

\frac{d}{d x} (\frac{250 x}{x + 3})

x \to 0 - lim (\frac{1}{1 + e \frac{1}{x}})

2 + 5 x

\frac{\partial}{\partial x} (\frac{q ( x , r , s , t ) x + r}{s x + t})

\frac{d}{d x} (sinh (cosh (x)))

What is the derivative of ln(x^{12}) ?
The derivative of ln(x^{12}) is (12)/x
What is the first derivative of ln(x^{12}) ?
The first derivative of ln(x^{12}) is (12)/x