What is the derivative of (sin(5x)/5) ?

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

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

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

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

cos (5 x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{5} cos (5 x) \cdot 5 : cos (5 x)

= cos (5 x)

\int (2 x^{2} - 3 x + 2) d x

x \to m + lim ([x])

y = (e^{2 x})^{2}

\frac{d}{d x} (x^{2} + 3 y^{2} - 3)

\frac{d y}{d t} + 5 y = 0

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