Question

F(x)=sinx+cosx найти производную функции f(f(x)) и не нужно удалять эту задачу модераторы, если вы не можете решить дайти другим попробовать

Answer 1

(sin(sinx+cosx)+cos(sinx+cosx))'=(cos(sinx+cosx))*(sinx+cosx)'-

sin(sinx+cosx)(sinx+cosx)'=

(cos(sinx+cosx))*(cosx-sinx)-sin(sinx+cosx)(cosx-sinx)=

(cosx-sinx)*((cos(sinx+cosx)-sin(sinx+cosx))

Answer 2

Calculating the Derivative of f(f(x))

To find the derivative of the function f(f(x)), we first need to find the derivative of the function f(x) and then substitute f(x) into the resulting derivative.

Given the function f(x) = sin(x) + cos(x), let's start by finding its derivative.

Finding the Derivative of f(x)

The derivative of the function f(x) can be found using the sum rule and the derivatives of sine and cosine functions.

The derivative of sin(x) is cos(x), and the derivative of cos(x) is -sin(x).

Therefore, the derivative of f(x) = sin(x) + cos(x) is: f'(x) = cos(x) - sin(x) [[1]]

Calculating the Derivative of f(f(x))

Now that we have the derivative of f(x), we can substitute f(x) into f'(x) to find the derivative of f(f(x)).

The derivative of f(f(x)) is: f'(f(x)) = cos(f(x)) - sin(f(x)) [[1]]

So, the derivative of f(f(x)) is cos(f(x)) - sin(f(x)).