Question

Найти производную функции f(x)=sin3x * cos3x

Answer 1

F(x)=sin3x*cos3x
f(x)=1/2 * 2sin3x*cos3x
f(x)=1/2* sin6x


f'(x)=(1/2 *sin6x)'=1/2 *(sin6x)' = 3cos6x

Answer 2

Finding the Derivative of f(x) = sin(3x) + cos(3x)

To find the derivative of the function f(x) = sin(3x) + cos(3x), we can use the chain rule. The chain rule states that if we have a composition of functions, the derivative is the product of the derivative of the outer function and the derivative of the inner function.

In this case, the outer function is the sum of sin(3x) and cos(3x), and the inner function is 3x. Let's find the derivative step by step:

1. The derivative of sin(3x) is found by applying the chain rule. The derivative of sin(u) with respect to u is cos(u), and the derivative of 3x with respect to x is 3. Therefore, the derivative of sin(3x) is cos(3x) * 3 = 3cos(3x).

2. Similarly, the derivative of cos(3x) is found by applying the chain rule. The derivative of cos(u) with respect to u is -sin(u), and the derivative of 3x with respect to x is 3. Therefore, the derivative of cos(3x) is -sin(3x) * 3 = -3sin(3x).

3. Finally, we add the derivatives of sin(3x) and cos(3x) to find the derivative of f(x). The derivative of f(x) = sin(3x) + cos(3x) is 3cos(3x) - 3sin(3x).

Therefore, the derivative of f(x) = sin(3x) + cos(3x) is 3cos(3x) - 3sin(3x).

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