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Popular >

derivative of arctan(3/(x+2))

Solution

\frac{d}{d x} (arctan (\frac{3}{x + 2}))

Solution

- \frac{3}{x ^{2} + 4 x + 13}

Solution steps

\frac{d}{d x} (arctan (\frac{3}{x + 2}))

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( \frac{3}{x + 2} ) ^{2} + 1} (- \frac{3}{( x + 2 ) ^{2}}) : - \frac{3}{x ^{2} + 4 x + 13}

= - \frac{3}{x ^{2} + 4 x + 13}

Popular Examples

integral of (sin(x))/(2+cos(x))

\int \frac{sin ( x )}{2 + cos ( x )} d x

tangent of f(x)=(x^2+15)(2x+18)tangent of

f (x) = (x^{2} + 15) (2 x + 18)

integral of (16)/(1+x^2)

\int \frac{16}{1 + x ^{2}} d x

(dy)/(dx)=2(1-y)

\frac{d y}{d x} = 2 (1 - y)

(\partial)/(\partial y)((-1)/(x^2+y^2))

\frac{\partial}{\partial y} (\frac{- 1}{x ^{2} + y ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of arctan(3/(x+2)) ?
The derivative of arctan(3/(x+2)) is -3/(x^2+4x+13)
What is the first derivative of arctan(3/(x+2)) ?
The first derivative of arctan(3/(x+2)) is -3/(x^2+4x+13)