Question

Найти y'(0), если y(x)=(x+3)cos2x

Answer 1

Y'(x)=cos2x+(x+3)*(-2sin2x)
y'(0)=1

Answer 2

To find the derivative of y(x), we can use the product rule and chain rule. Let's differentiate each part separately and then evaluate it at x = 0.

Given: y(x) = (x + 3)cos(2x)

Using the product rule, the derivative of y(x) is:

y'(x) = (x + 3)(-sin(2x)) + cos(2x)(1)

Now let's evaluate y'(x) at x = 0:

y'(0) = (0 + 3)(-sin(20)) + cos(20)(1) = 3(-sin(0)) + cos(0) = 3(0) + 1 = 0 + 1 = 1

Therefore, y'(0) = 1.