What is the derivative of ln(x^3-63) ?

The derivative of ln(x^3-63) is (3x^2)/(x^3-63)

What is the first derivative of ln(x^3-63) ?

The first derivative of ln(x^3-63) is (3x^2)/(x^3-63)

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\frac{d}{d x} (ln (x^{3} - 63))

\frac{3 x ^{2}}{x ^{3} - 63}

Solution steps

\frac{d}{d x} (ln (x^{3} - 63))

Apply the chain rule:

\frac{1}{x ^{3} - 63} \frac{d}{d x} (x^{3} - 63)

= \frac{1}{x ^{3} - 63} \frac{d}{d x} (x^{3} - 63)

\frac{d}{d x} (x^{3} - 63) = 3 x^{2}

= \frac{1}{x ^{3} - 63} \cdot 3 x^{2}

Simplify

\frac{1}{x ^{3} - 63} \cdot 3 x^{2} : \frac{3 x ^{2}}{x ^{3} - 63}

= \frac{3 x ^{2}}{x ^{3} - 63}

What is the derivative of ln(x^3-63) ?
The derivative of ln(x^3-63) is (3x^2)/(x^3-63)
What is the first derivative of ln(x^3-63) ?
The first derivative of ln(x^3-63) is (3x^2)/(x^3-63)