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

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

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

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

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derivative of

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

cos (\frac{x}{5})

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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