Find the derivative of y=sin(pi x)

Bergen

Bergen

Answered question

2021-02-05

Find the derivative of
y=sin(πx)

Answer & Explanation

mhalmantus

mhalmantus

Skilled2021-02-06Added 105 answers

If you're in a different section of your course, please let me know in a comment. This is an implementation of the chain rule. Keep in mind that the chain rule essentially states that you must first multiply the derivatives of the "inside" and "outside" functions independently.
The outside function here is f(x)=sin(x). Keep in mind that its derivative cos(x)
The inside function is g(x)=πx. The derivative of this is clearly π.
Putting these together we get f=cos(πx)×π=πcos(πx) where the πx in the coscos function is derived from the requirement that, when multiplying, the identical argument from the external function be inserted.
If that doesn't make sense, please let me know.

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