What is the derivative of y=2sin(pix-y) ?

The derivative of y=2sin(pix-y) is 2cos(pix-y)pi

What is the first derivative of y=2sin(pix-y) ?

The first derivative of y=2sin(pix-y) is 2cos(pix-y)pi

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derivative

2 cos (π x - y) π

Solution steps

\frac{d}{d x} (2 sin (π x - y))

Treat

y

as a constant

Take the constant out:

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

= 2 \frac{d}{d x} (sin (π x - y))

Apply the chain rule:

cos (π x - y) \frac{d}{d x} (π x - y)

= cos (π x - y) \frac{d}{d x} (π x - y)

\frac{d}{d x} (π x - y) = π

= 2 cos (π x - y) π

What is the derivative of y=2sin(pix-y) ?
The derivative of y=2sin(pix-y) is 2cos(pix-y)pi
What is the first derivative of y=2sin(pix-y) ?
The first derivative of y=2sin(pix-y) is 2cos(pix-y)pi