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

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

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

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

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

cos (5 x)

Solution steps

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

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 \frac{x ^{2} + 1}{x ^{2} ( x - 1 )} d x

\int \frac{4 x + 10}{x ^{3}} d x

\int \frac{2 e ^{2 x}}{1 + e ^{4 x}} d x

\frac{d y}{d x} = 5 - 8 x

\int \frac{a ^{x}}{b ^{x}} d x

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