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Popular >

derivative of f(x)=arctan(x/a)

Solution

derivative of

f (x) = arctan (\frac{x}{a})

Solution

\frac{a}{x ^{2} + a ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{a}{x ^{2} + a ^{2}}

Popular Examples

derivative of cosh^3(x)

\frac{d}{d x} (cosh^{3} (x))

integral of (10x+6)

\int (10 x + 6) d x

derivative of (x^2/5)

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

integral of (5ln(x))/(x^3)

\int \frac{5 ln ( x )}{x ^{3}} d x

y^{''}-2y^'-15y=3cos(2x)+4x^2

y^{^{''}} - 2 y^{^{'}} - 15 y = 3 cos (2 x) + 4 x^{2}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=arctan(x/a) ?
The derivative of f(x)=arctan(x/a) is a/(x^2+a^2)
What is the first derivative of f(x)=arctan(x/a) ?
The first derivative of f(x)=arctan(x/a) is a/(x^2+a^2)