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Popular >

derivative of ln(arctan(x))

Solution

derivative of

ln (arctan (x))

Solution

\frac{1}{arctan ( x ) ( x ^{2} + 1 )}

Solution steps

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

Apply the chain rule:

\frac{1}{arctan ( x )} \frac{d}{d x} (arctan (x))

= \frac{1}{arctan ( x )} \frac{d}{d x} (arctan (x))

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

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

Simplify

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

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

Popular Examples

(dy)/(dx)=2+1/x ,y(1)=5

\frac{d y}{d x} = 2 + \frac{1}{x}, y (1) = 5

y^'+2xy=2x^3,y(0)=2

y^{^{'}} + 2 x y = 2 x^{3}, y (0) = 2

inverse oflaplace-(1.25)/(s+2)inverse laplace

- \frac{1.25}{s + 2}

integral of x/(sqrt(8+x^2))+3e^{4x}

\int \frac{x}{8 + x ^{2}} + 3 e^{4 x} d x

integral of x^2ln(x^6-1)

\int x^{2} ln (x^{6} - 1) d x

Frequently Asked Questions (FAQ)

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