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

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

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

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

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

45 cos (9 x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

cos (9 x) \frac{d}{d x} (9 x)

= cos (9 x) \frac{d}{d x} (9 x)

\frac{d}{d x} (9 x) = 9

= 5 cos (9 x) \cdot 9

Simplify

= 45 cos (9 x)

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