Question

Y'=(5*cos7x)' как это решить?

Answer 1

y'=(5*cos7x)'= 5*(-sin7х)*7= -35sin7х

Answer 2

To find the derivative of the function Y = 5*cos(7x), you can use the chain rule. The chain rule states that if you have a function of the form f(g(x)), the derivative is given by f'(g(x)) * g'(x).

In this case, f(u) = 5*cos(u) and g(x) = 7x. Therefore, we have:

Y' = f'(g(x)) * g'(x)

To find f'(u), the derivative of 5*cos(u) with respect to u, we can use the derivative of the cosine function, which is -sin(u):

f'(u) = -5*sin(u)

Next, we find g'(x), the derivative of 7x with respect to x, which is simply 7:

g'(x) = 7

Now we can substitute these values back into the chain rule formula:

Y' = f'(g(x)) * g'(x) = (-5sin(7x)) * 7 = -35sin(7x)

Therefore, the derivative of Y = 5cos(7x) is Y' = -35sin(7x).