Question

Differentiate w.r.t.x : 1-cosx/1+cosx​

Answer 1

Step-by-step explanation:

The derivative of cos(x) is -sin(x).Step 1: The first thing we want to do is identify the function in the numerator of 1/cos(x). We see this is 1, so we say f(x) = 1. We now want to find the derivative of this function. Since 1 is a constant, we know the derivative is 0 from our fact list. Therefore, f'(x) = 0.

Step 2: Our next step is to identify the function in the denominator of 1/cos(x). The function in the denominator is cos(x), so we let g(x) = cos(x). Now we find the derivative of cos(x), which our fact list says is -sin(x). Thus, g'(x) = -sin(x).

Step 3: Our last step is to plug f, g, f', and g' that we found in steps 1 and 2 into the quotient rule.

plugging in

Lastly, we simplify. To do this, we will use our two facts that 1/cos(x) = sec(x)

and that sin(x) / cos(x) = tan(x).

simplifying

We see that the derivative of 1/cos(x) is sec(x)tan(x)