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Popular >

derivative of arctan(x/5)

Solution

derivative of

arctan (\frac{x}{5})

Solution

\frac{5}{x ^{2} + 25}

Solution steps

\frac{d}{d x} (arctan (\frac{x}{5}))

Apply the chain rule:

\frac{1}{( \frac{x}{5} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{5})

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

\frac{d}{d x} (\frac{x}{5}) = \frac{1}{5}

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

Simplify

\frac{1}{( \frac{x}{5} ) ^{2} + 1} \cdot \frac{1}{5} : \frac{5}{x ^{2} + 25}

= \frac{5}{x ^{2} + 25}

Popular Examples

integral from-1 to 0 of 1/(x^3)

\int_{- 1}^{0} \frac{1}{x ^{3}} d x

derivative of (1/(x^2-6/(x^4))(x+8x^3))

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{6}{x ^{4}}) (x + 8 x^{3}))

limit as x approaches 1 of 0/(x^2-1)

x \to 1 lim (\frac{0}{x ^{2} - 1})

integral of (18x+5)

\int (18 x + 5) d x

integral of 2e^{3x}

\int 2 e^{3 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of arctan(x/5) ?
The derivative of arctan(x/5) is 5/(x^2+25)
What is the first derivative of arctan(x/5) ?
The first derivative of arctan(x/5) is 5/(x^2+25)