What is the derivative of 1/5 cos(5x) ?

The derivative of 1/5 cos(5x) is -sin(5x)

What is the first derivative of 1/5 cos(5x) ?

The first derivative of 1/5 cos(5x) is -sin(5x)

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\frac{d}{d x} (\frac{1}{5} cos (5 x))

- sin (5 x)

Solution steps

\frac{d}{d x} (\frac{1}{5} cos (5 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{5} \frac{d}{d x} (cos (5 x))

Apply the chain rule:

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

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

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

= \frac{1}{5} (- sin (5 x) \cdot 5)

Simplify

\frac{1}{5} (- sin (5 x) \cdot 5) : - sin (5 x)

= - sin (5 x)

What is the derivative of 1/5 cos(5x) ?
The derivative of 1/5 cos(5x) is -sin(5x)
What is the first derivative of 1/5 cos(5x) ?
The first derivative of 1/5 cos(5x) is -sin(5x)