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Popular >

derivative of ln(x^4-6x^2)

Solution

\frac{d}{d x} (ln (x^{4} - 6 x^{2}))

Solution

\frac{4 ( x ^{2} - 3 )}{x ( x ^{2} - 6 )}

Solution steps

\frac{d}{d x} (ln (x^{4} - 6 x^{2}))

Apply the chain rule:

\frac{1}{x ^{4} - 6 x ^{2}} \frac{d}{d x} (x^{4} - 6 x^{2})

= \frac{1}{x ^{4} - 6 x ^{2}} \frac{d}{d x} (x^{4} - 6 x^{2})

\frac{d}{d x} (x^{4} - 6 x^{2}) = 4 x^{3} - 12 x

= \frac{1}{x ^{4} - 6 x ^{2}} (4 x^{3} - 12 x)

Simplify

\frac{1}{x ^{4} - 6 x ^{2}} (4 x^{3} - 12 x) : \frac{4 ( x ^{2} - 3 )}{x ( x ^{2} - 6 )}

= \frac{4 ( x ^{2} - 3 )}{x ( x ^{2} - 6 )}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(x^4-6x^2) ?
The derivative of ln(x^4-6x^2) is (4(x^2-3))/(x(x^2-6))
What is the first derivative of ln(x^4-6x^2) ?
The first derivative of ln(x^4-6x^2) is (4(x^2-3))/(x(x^2-6))