If y = cos 3x, find δyδx
A. 13sin3x
B. −13sin3x
C. 3 sin 3x
D. -3 sin 3x
We start by using the chain rule.
The derivative of the cosine function is the negative sine function. So, the derivative of y = cos 3x with respect to x is:
dy/dx = -sin 3x
Therefore, the answer is D. -3sin3x
To find δy/δx, we need to differentiate y = cos 3x with respect to x.
Using the chain rule, we differentiate cos 3x as follows:
dy/dx = d/dx(cos 3x)
= -sin 3x * d/dx(3x)
= -sin 3x * 3
= -3 sin 3x
Therefore, the answer is D. -3 sin 3x.