What is the derivative of arctan(ln(4x^3)) ?

The derivative of arctan(ln(4x^3)) is (6ln(2)x^2)/(4ln^2(2)x^6+1)

What is the first derivative of arctan(ln(4x^3)) ?

The first derivative of arctan(ln(4x^3)) is (6ln(2)x^2)/(4ln^2(2)x^6+1)

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\frac{d}{d x} (arctan (ln (4) x^{3}))

\frac{6 ln ( 2 ) x ^{2}}{4 ln ^{2} ( 2 ) x ^{6} + 1}

Solution steps

\frac{d}{d x} (arctan (ln (4) x^{3}))

Simplify

arctan (ln (4) x^{3}) : arctan (2 ln (2) x^{3})

= \frac{d}{d x} (arctan (2 ln (2) x^{3}))

Apply the chain rule:

\frac{1}{( 2 ln ( 2 ) x ^{3} ) ^{2} + 1} \frac{d}{d x} (2 ln (2) x^{3})

= \frac{1}{( 2 ln ( 2 ) x ^{3} ) ^{2} + 1} \frac{d}{d x} (2 ln (2) x^{3})

\frac{d}{d x} (2 ln (2) x^{3}) = 6 ln (2) x^{2}

= \frac{1}{( 2 ln ( 2 ) x ^{3} ) ^{2} + 1} \cdot 6 ln (2) x^{2}

Simplify

\frac{1}{( 2 ln ( 2 ) x ^{3} ) ^{2} + 1} \cdot 6 ln (2) x^{2} : \frac{6 ln ( 2 ) x ^{2}}{4 ln ^{2} ( 2 ) x ^{6} + 1}

= \frac{6 ln ( 2 ) x ^{2}}{4 ln ^{2} ( 2 ) x ^{6} + 1}

What is the derivative of arctan(ln(4x^3)) ?
The derivative of arctan(ln(4x^3)) is (6ln(2)x^2)/(4ln^2(2)x^6+1)
What is the first derivative of arctan(ln(4x^3)) ?
The first derivative of arctan(ln(4x^3)) is (6ln(2)x^2)/(4ln^2(2)x^6+1)