Question

Найдите производную функции: f (x) = 3 cos 2x; y (x) = 4 tg 3x. ПОМОГИТЕ

Answer 1

F´(x) = (3 cos 2x)´ = 3*(- sin2x)* 2 = - 6sin2x         

 

y´(x) = (4 tg 3x)´ = 4*1/cos²3x* 3 = 12/cos²3x       

Answer 2

Derivative of f(x) = 3 cos(2x):

To find the derivative of the function f(x) = 3 cos(2x), we can use the chain rule. The chain rule states that if we have a composite function, f(g(x)), then the derivative of f(g(x)) with respect to x is equal to the derivative of f(g(x)) with respect to g(x), multiplied by the derivative of g(x) with respect to x.

In this case, f(x) = 3 cos(2x), so we can let g(x) = 2x. The derivative of cos(2x) with respect to x is -2 sin(2x), and the derivative of 2x with respect to x is 2. Therefore, the derivative of f(x) = 3 cos(2x) is:

f'(x) = 3 * (-2 sin(2x)) * 2 = -12 sin(2x).

Derivative of y(x) = 4 tg(3x):

To find the derivative of the function y(x) = 4 tg(3x), we can again use the chain rule. Let g(x) = 3x. The derivative of tg(3x) with respect to x is 3 sec^2(3x), and the derivative of 3x with respect to x is 3. Therefore, the derivative of y(x) = 4 tg(3x) is:

y'(x) = 4 * (3 sec^2(3x)) * 3 = 36 sec^2(3x).

So, the derivatives of the given functions are: - f'(x) = -12 sin(2x) - y'(x) = 36 sec^2(3x)