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)

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = - 3

y y^{^{'}} - 6 e^{x} = 0

\int sec (1) d x

x \to \frac{x}{4} lim (\frac{sin ( x )}{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)