What is the derivative of 9sin(5x) ?

The derivative of 9sin(5x) is 45cos(5x)

What is the first derivative of 9sin(5x) ?

The first derivative of 9sin(5x) is 45cos(5x)

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\frac{d}{d x} (9 sin (5 x))

45 cos (5 x)

Solution steps

\frac{d}{d x} (9 sin (5 x))

Take the constant out:

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

= 9 \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

= 9 cos (5 x) \cdot 5

Simplify

= 45 cos (5 x)

What is the derivative of 9sin(5x) ?
The derivative of 9sin(5x) is 45cos(5x)
What is the first derivative of 9sin(5x) ?
The first derivative of 9sin(5x) is 45cos(5x)