# How do you differentiate #f(x)=(x+2)/cosx#?

To differentiate this, we will use the quotient rule. The quotient rule states that the derivative of a function that is one function divided by another, such as

has a derivative of

So, for the given function of

We can say that

Taking the derivative of both of these, we see that

Applying these to the quotient rule, this becomes

Simplifying:

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To differentiate f(x) = (x + 2) / cos(x), you can use the quotient rule, which states that if you have a function in the form f(x) = u(x) / v(x), then f'(x) = [u'(x)v(x) - u(x)v'(x)] / [v(x)]^2. Applying this rule to the given function, we first find the derivatives of the numerator and denominator separately.

Let u(x) = x + 2 and v(x) = cos(x). Then, u'(x) = 1 (since the derivative of x with respect to x is 1) and v'(x) = -sin(x) (since the derivative of cos(x) is -sin(x)).

Now, applying the quotient rule:

f'(x) = [u'(x)v(x) - u(x)v'(x)] / [v(x)]^2 = [(1)(cos(x)) - (x + 2)(-sin(x))] / [cos(x)]^2 = [cos(x) + (x + 2)sin(x)] / cos^2(x)

So, the derivative of f(x) = (x + 2) / cos(x) is f'(x) = [cos(x) + (x + 2)sin(x)] / cos^2(x).

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