Question

F(x) = 5*(sinx - cosx) + √2 * cos5x.значения х производной

Answer 1

Ответ : на фото

Объяснение :

Answer 2

To find the derivative of the function f(x) = 5*(sin(x) - cos(x)) + √2 * cos(5x), we'll differentiate each term separately using the rules of differentiation. Let's begin:

1. The derivative of 5*(sin(x) - cos(x)) can be found by applying the product rule. Let's denote g(x) = sin(x) - cos(x):

g'(x) = (sin(x))' - (cos(x))' = cos(x) + sin(x)

Now, using the product rule, the derivative of f(x) with respect to x is:

f'(x) = 5 * g'(x) = 5 * (cos(x) + sin(x))

2. The derivative of √2 * cos(5x) can be found using the chain rule. Let's denote h(x) = cos(5x):

h'(x) = (cos(5x))' * (5x)' = -sin(5x) * 5 = -5sin(5x)

Now, using the chain rule, the derivative of √2 * cos(5x) with respect to x is:

[√2 * cos(5x)]' = √2 * h'(x) = √2 * (-5sin(5x)) = -5√2sin(5x)

Therefore, the derivative of f(x) = 5*(sin(x) - cos(x)) + √2 * cos(5x) with respect to x is:

f'(x) = 5 * (cos(x) + sin(x)) - 5√2sin(5x)

These are the values of the derivative for different values of x.