derivative of cos(arctan(3x)) — step-by-step solution

⚠ 3x is read as the product 3*x: for a power, write 3^x

Let's differentiate:

\frac{d}{d x} (\cos (\arctan (3 x)))

Apply the differentiation rule:

\frac{d}{d x} (\cos (f)) = - \frac{d}{d x} (f) \cdot \sin (f)

with f =

\arctan (3 x)

- \frac{d}{d x} (\arctan (3 x)) \cdot \sin (\arctan (3 x))

Apply the differentiation rule:

\frac{d}{d x} (\arctan (f)) = \frac{d}{d x} (f) \cdot \frac{1}{f^{2} + 1}

with f =

3 x

- \frac{\frac{d}{d x} (3 x)}{{(3 x)}^{2} + 1} \cdot \sin (\arctan (3 x))

ℹ

- \frac{\frac{d}{d x} (3 x)}{{(3 x)}^{2} + 1} \cdot \sin (\arctan (3 x))

- \frac{\frac{d}{d x} (3 x) \cdot \sin (\arctan (3 x))}{{(3 x)}^{2} + 1}

‖

\frac{d}{d x} (3 x)

3

- \frac{3 \cdot \sin (\arctan (3 x))}{{(3 x)}^{2} + 1}

- \frac{3 \cdot \sin (\arctan (3 x))}{3^{2} \cdot x^{2} + 1}

▶Derivative:

- \frac{3 \cdot \sin (\arctan (3 x))}{9 x^{2} + 1}