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Popular >

derivative of arctan((2x)/5)

Solution

derivative of

arctan (\frac{2 x}{5})

Solution

\frac{10}{4 x ^{2} + 25}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( \frac{2 x}{5} ) ^{2} + 1} \cdot \frac{2}{5} : \frac{10}{4 x ^{2} + 25}

= \frac{10}{4 x ^{2} + 25}

Popular Examples

derivative of 4xsqrt(3x^2+2)derivative of

4 x 3 x^{2} + 2

derivative of (x^5)/(10)+1/(6x^3)derivative of

\frac{x ^{5}}{10} + \frac{1}{6 x ^{3}}

t*(dy)/(dt)=t^3+14t^3y

t \cdot \frac{d y}{d t} = t^{3} + 14 t^{3} y

integral of (cos(t))/(sin^4(t)-16)

\int \frac{cos ( t )}{sin ^{4} ( t ) - 16} d t

derivative of (x+5/(x+1))

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

Frequently Asked Questions (FAQ)

What is the derivative of arctan((2x)/5) ?
The derivative of arctan((2x)/5) is (10)/(4x^2+25)
What is the first derivative of arctan((2x)/5) ?
The first derivative of arctan((2x)/5) is (10)/(4x^2+25)