Question

Как взять производную? cos (2x^2)

Answer 1

Как производную сложной функции. Производная косинуса равна минус синусу этого же аргумента и умножаем на производную аргумента:
(сos (2x²))`=-sin(2x²)·(2x²)`=- 4x·sin(2x²)

Answer 2

How to take the derivative of cos(2x^2)?

To find the derivative of the function cos(2x^2), we can use the chain rule. The chain rule states that if we have a composite function, such as f(g(x)), the derivative can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.

In this case, the outer function is cos(x), and the inner function is 2x^2. Let's find the derivative step by step:

1. Take the derivative of the outer function cos(x), which is -sin(x). 2. Multiply it by the derivative of the inner function 2x^2, which is 4x.

Therefore, the derivative of cos(2x^2) is -4x*sin(2x^2).