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

Simplify

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

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

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

\frac{d y}{d x} + y = y x e^{x + 2}

\int e^{x} 9 - e^{x} d x

\frac{d y}{d x} = - \frac{2 x y + 1}{x ^{2} + 2 y}

\int \frac{2 t ^{2}}{2 t ^{2} + 1} d t

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)