Question

(1/cosx)' решите производную ​

Answer 1

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Answer 2

To find the derivative of (1/cos(x)), we'll use the quotient rule of differentiation. The quotient rule states that if we have a function of the form f(x) = g(x)/h(x), then its derivative f'(x) is given by:

f'(x) = (g'(x) * h(x) - g(x) * h'(x)) / [h(x)]^2

In our case, g(x) = 1 and h(x) = cos(x). Let's find the derivatives of g(x) and h(x):

g'(x) = d/dx(1) = 0 (since the derivative of a constant is zero) h'(x) = d/dx(cos(x)) = -sin(x)

Now, we can apply the quotient rule:

(1/cos(x))' = (0 * cos(x) - 1 * (-sin(x))) / [cos(x)]^2 = sin(x) / [cos(x)]^2

So, the derivative of (1/cos(x)) is sin(x) / [cos(x)]^2.