What is the derivative of ln(x^{61}) ?

The derivative of ln(x^{61}) is (61)/x

What is the first derivative of ln(x^{61}) ?

The first derivative of ln(x^{61}) is (61)/x

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derivative of

ln (x^{61})

\frac{61}{x}

Solution steps

\frac{d}{d x} (ln (x^{61}))

Apply the chain rule:

\frac{1}{x ^{61}} \frac{d}{d x} (x^{61})

= \frac{1}{x ^{61}} \frac{d}{d x} (x^{61})

\frac{d}{d x} (x^{61}) = 61 x^{60}

= \frac{1}{x ^{61}} \cdot 61 x^{60}

Simplify

\frac{1}{x ^{61}} \cdot 61 x^{60} : \frac{61}{x}

= \frac{61}{x}

\frac{d}{d x} (\frac{5 x}{x ^{2} + 5})

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x \to 5 - lim (\frac{2}{( x - 5 ) ^{3}})

\frac{d}{d x} (\frac{sin ( x )}{3 x ^{2}})

What is the derivative of ln(x^{61}) ?
The derivative of ln(x^{61}) is (61)/x
What is the first derivative of ln(x^{61}) ?
The first derivative of ln(x^{61}) is (61)/x