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Popular >

derivative of arctan(ln(x^2))

Solution

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

Solution

\frac{2}{x ( 4 ln ^{2} ( x ) + 1 )}

Solution steps

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

Apply the chain rule:

\frac{1}{( ln ( x ^{2} ) ) ^{2} + 1} \frac{d}{d x} (ln (x^{2}))

= \frac{1}{( ln ( x ^{2} ) ) ^{2} + 1} \frac{d}{d x} (ln (x^{2}))

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

= \frac{1}{( ln ( x ^{2} ) ) ^{2} + 1} \cdot \frac{2}{x}

Simplify

\frac{1}{ln ^{2} ( x ^{2} ) + 1} \cdot \frac{2}{x} : \frac{2}{x ( 4 ln ^{2} ( x ) + 1 )}

= \frac{2}{x ( 4 ln ^{2} ( x ) + 1 )}

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

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\int \frac{8}{x + 1} d x

(\partial)/(\partial x)(5/(5x+3y))

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\frac{10}{s ( s + 2 ) ( s + 3 ) ^{2}}

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

Frequently Asked Questions (FAQ)

What is the derivative of arctan(ln(x^2)) ?
The derivative of arctan(ln(x^2)) is 2/(x(4ln^2(x)+1))
What is the first derivative of arctan(ln(x^2)) ?
The first derivative of arctan(ln(x^2)) is 2/(x(4ln^2(x)+1))