Question

How to find the derivative of the following function: 5sin(4pix)
Is this the product rule?

Answer 1

Nothing to do with product rule. Its chain rule, if youve been introduced to it.

Answer 2

I have, so I would take the derivative of the outside, which is 5 right? and then take the derivative of sin which is cos. and finally take the derivative of 4pix which is 4pi. Is that correct?

Answer 3

d/dx(5⋅sin(4π⋅x))
=5⋅d/dx(sin(4π⋅x))
=5⋅cos(4π⋅x)⋅d/dx(4π⋅x)
=5⋅4π⋅cos(4π⋅x)
=20π⋅cos(4π⋅x)

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Answer 4

The 5 means nothing really, it just tags along. But yeah, just taking the derivatives of each layer or inner function and multiplying the results. Outer function is sin, differentiates to cos, inner function is 4pix, differentiates to 4pi, chain rules multiplies the results of those derivatives, giving you 20picos(4pix), right.

Answer 5

Thank you!