Question

(cos10x)' производная

Answer 1

$(cos10x)' = -sin10x * (10x)' = -10*sin10x$

Answer 2

To find the derivative of the function f(x) = cos(10x) with respect to x, we'll use the chain rule. The chain rule states that if we have a function g(u) and another function f(x) where u depends on x, then the derivative of the composite function g(f(x)) with respect to x is given by g'(u) * f'(x).

In this case, g(u) = cos(u) and f(x) = 10x. So, g'(u) = -sin(u) and f'(x) = 10.

Now, we can find the derivative of f(x) = cos(10x) as follows:

f'(x) = g'(f(x)) * f'(x) = -sin(10x) * 10

So, the derivative of cos(10x) with respect to x is:

f'(x) = -10sin(10x)