What is (\partial)/(\partial x)(arctan(5x)) ?

The answer to (\partial)/(\partial x)(arctan(5x)) is 5/(25x^2+1)

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(\partial)/(\partial x)(arctan(5x))

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

\frac{5}{25 x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (5 x) = 5

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

Simplify

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

= \frac{5}{25 x ^{2} + 1}

(9 y^{2} - x y) d x + x^{2} d y = 0

\int \frac{1}{x ^{2} + 10 x + 29} d x

f (x) = (arcsec (x))^{13}

\int 3 x sin^{2} (x) d x

\int_{0}^{1} - \frac{1}{x - 5} + \frac{2}{x - 2} d x

What is (\partial)/(\partial x)(arctan(5x)) ?
The answer to (\partial)/(\partial x)(arctan(5x)) is 5/(25x^2+1)