What is the derivative of 5sin(10x) ?

The derivative of 5sin(10x) is 50cos(10x)

What is the first derivative of 5sin(10x) ?

The first derivative of 5sin(10x) is 50cos(10x)

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\frac{d}{d x} (5 sin (10 x))

50 cos (10 x)

Solution steps

\frac{d}{d x} (5 sin (10 x))

Take the constant out:

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

= 5 \frac{d}{d x} (sin (10 x))

Apply the chain rule:

cos (10 x) \frac{d}{d x} (10 x)

= cos (10 x) \frac{d}{d x} (10 x)

\frac{d}{d x} (10 x) = 10

= 5 cos (10 x) \cdot 10

Simplify

= 50 cos (10 x)

What is the derivative of 5sin(10x) ?
The derivative of 5sin(10x) is 50cos(10x)
What is the first derivative of 5sin(10x) ?
The first derivative of 5sin(10x) is 50cos(10x)