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

The derivative of arctan(4ln(x)) is 4/(x(16ln^2(x)+1))

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

The first derivative of arctan(4ln(x)) is 4/(x(16ln^2(x)+1))

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derivative of

arctan (4 ln (x))

\frac{4}{x ( 16 ln ^{2} ( x ) + 1 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 ln (x)) = \frac{4}{x}

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

Simplify

\frac{1}{( 4 ln ( x ) ) ^{2} + 1} \cdot \frac{4}{x} : \frac{4}{x ( 16 ln ^{2} ( x ) + 1 )}

= \frac{4}{x ( 16 ln ^{2} ( x ) + 1 )}

174

\int \frac{4 x + 4}{( x ^{2} + 2 x + 3 ) ^{2}} d x

f (x) = 6 x, at x = 6

\int \frac{t}{t ^{2} - 1} d t

f (x) = \frac{4}{x}, at 9 \frac{4}{9}

What is the derivative of arctan(4ln(x)) ?
The derivative of arctan(4ln(x)) is 4/(x(16ln^2(x)+1))
What is the first derivative of arctan(4ln(x)) ?
The first derivative of arctan(4ln(x)) is 4/(x(16ln^2(x)+1))