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Popular >

derivative of arctan(x/3)

Solution

derivative of

arctan (\frac{x}{3})

Solution

\frac{3}{x ^{2} + 9}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{3}) = \frac{1}{3}

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

Simplify

\frac{1}{( \frac{x}{3} ) ^{2} + 1} \cdot \frac{1}{3} : \frac{3}{x ^{2} + 9}

= \frac{3}{x ^{2} + 9}

Popular Examples

derivative of f(x)=x+sqrt(x)+2 derivative of

f (x) = x + x + 2

(\partial)/(\partial x)(xy(x-2)(y+3))

\frac{\partial}{\partial x} (x y (x - 2) (y + 3))

integral of xln(x+5)

\int x ln (x + 5) d x

(\partial)/(\partial x)(ln(x^2+y^5))

\frac{\partial}{\partial x} (ln (x^{2} + y^{5}))

integral of ln(sqrt(x+2))

\int ln (x + 2) d x

Frequently Asked Questions (FAQ)

What is the derivative of arctan(x/3) ?
The derivative of arctan(x/3) is 3/(x^2+9)
What is the first derivative of arctan(x/3) ?
The first derivative of arctan(x/3) is 3/(x^2+9)