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Popular >

derivative of arctan(x+2)

Solution

\frac{d}{d x} (arctan (x + 2))

Solution

\frac{1}{x ^{2} + 4 x + 5}

Solution steps

\frac{d}{d x} (arctan (x + 2))

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x ^{2} + 4 x + 5}

Popular Examples

derivative of sin(x-y)

\frac{d}{d x} (sin (x - y))

integral of (20x^3)/(3+5x^4)

\int \frac{20 x ^{3}}{3 + 5 x ^{4}} d x

(\partial)/(\partial x)(x^2-y^2+2xy)

\frac{\partial}{\partial x} (x^{2} - y^{2} + 2 x y)

derivative of (7x^3+x^2)^{2/3}derivative of

(7 x^{3} + x^{2})^{\frac{2}{3}}

(\partial)/(\partial x)((2x+7y)^{11})

\frac{\partial}{\partial x} ((2 x + 7 y)^{11})

Frequently Asked Questions (FAQ)

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