What is the derivative of arctan(5x) ?

The derivative of arctan(5x) is 5/(25x^2+1)

What is the first derivative of arctan(5x) ?

The first derivative of arctan(5x) is 5/(25x^2+1)

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derivative of

arctan (5 x)

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d 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}

\frac{d y}{d x} = x - x^{2}

f (x) = sin (x) + cos (x)

\int sin^{4} (3 x) d x

A e^{- 4}

\int \frac{x}{x ^{2} + x - 6} d x

What is the derivative of arctan(5x) ?
The derivative of arctan(5x) is 5/(25x^2+1)
What is the first derivative of arctan(5x) ?
The first derivative of arctan(5x) is 5/(25x^2+1)