What is the derivative of arctan(-4x) ?

The derivative of arctan(-4x) is -4/(16x^2+1)

What is the first derivative of arctan(-4x) ?

The first derivative of arctan(-4x) is -4/(16x^2+1)

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\frac{d}{d x} (arctan (- 4 x))

- \frac{4}{16 x ^{2} + 1}

Solution steps

\frac{d}{d x} (arctan (- 4 x))

Apply the chain rule:

\frac{1}{( - 4 x ) ^{2} + 1} \frac{d}{d x} (- 4 x)

= \frac{1}{( - 4 x ) ^{2} + 1} \frac{d}{d x} (- 4 x)

\frac{d}{d x} (- 4 x) = - 4

= \frac{1}{( - 4 x ) ^{2} + 1} (- 4)

Simplify

\frac{1}{( - 4 x ) ^{2} + 1} (- 4) : - \frac{4}{16 x ^{2} + 1}

= - \frac{4}{16 x ^{2} + 1}

f (x) = \frac{x ^{2} + 1}{2 x - 3}

\frac{d}{d x} (\frac{x ^{2}}{1 - x})

\int \frac{x ^{3}}{3} + x d x

\int cos (3 z + 4) d z

What is the derivative of arctan(-4x) ?
The derivative of arctan(-4x) is -4/(16x^2+1)
What is the first derivative of arctan(-4x) ?
The first derivative of arctan(-4x) is -4/(16x^2+1)