Question - Calculus - Derivative of y = 3 cos(2x)
Solution:
The image shows a calculus problem asking to find the derivative dy/dx of the function y with respect to x. The function given is:y = 3 cos(2x)To find the derivative of this function, we use the chain rule, which in this case involves differentiating the cosine function and then accounting for the inner function, 2x. The derivative of cos(u) with respect to u is -sin(u), and then we multiply this by the derivative of the inner function, which is 2 in this case.The derivative of y with respect to x is thus:dy/dx = -3 sin(2x) * 2Simplify the expression:dy/dx = -6 sin(2x)
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