What is the derivative of arctan(ln(4x^5)) ?

The derivative of arctan(ln(4x^5)) is (10ln(2)x^4)/(4ln^2(2)x^{10)+1}

What is the first derivative of arctan(ln(4x^5)) ?

The first derivative of arctan(ln(4x^5)) is (10ln(2)x^4)/(4ln^2(2)x^{10)+1}

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\frac{d}{d x} (arctan (ln (4) x^{5}))

\frac{10 ln ( 2 ) x ^{4}}{4 ln ^{2} ( 2 ) x ^{10} + 1}

Solution steps

\frac{d}{d x} (arctan (ln (4) x^{5}))

Simplify

arctan (ln (4) x^{5}) : arctan (2 ln (2) x^{5})

= \frac{d}{d x} (arctan (2 ln (2) x^{5}))

Apply the chain rule:

\frac{1}{( 2 ln ( 2 ) x ^{5} ) ^{2} + 1} \frac{d}{d x} (2 ln (2) x^{5})

= \frac{1}{( 2 ln ( 2 ) x ^{5} ) ^{2} + 1} \frac{d}{d x} (2 ln (2) x^{5})

\frac{d}{d x} (2 ln (2) x^{5}) = 10 ln (2) x^{4}

= \frac{1}{( 2 ln ( 2 ) x ^{5} ) ^{2} + 1} \cdot 10 ln (2) x^{4}

Simplify

\frac{1}{( 2 ln ( 2 ) x ^{5} ) ^{2} + 1} \cdot 10 ln (2) x^{4} : \frac{10 ln ( 2 ) x ^{4}}{4 ln ^{2} ( 2 ) x ^{10} + 1}

= \frac{10 ln ( 2 ) x ^{4}}{4 ln ^{2} ( 2 ) x ^{10} + 1}

What is the derivative of arctan(ln(4x^5)) ?
The derivative of arctan(ln(4x^5)) is (10ln(2)x^4)/(4ln^2(2)x^{10)+1}
What is the first derivative of arctan(ln(4x^5)) ?
The first derivative of arctan(ln(4x^5)) is (10ln(2)x^4)/(4ln^2(2)x^{10)+1}