d/dx (sec x)
To find the derivative of sec x with respect to x, we will use the quotient rule
To find the derivative of sec x with respect to x, we will use the quotient rule.
Recall that the derivative of a function f(x) = g(x)/h(x), where g(x) and h(x) are differentiable functions, is given by:
f'(x) = (g'(x) * h(x) – g(x) * h'(x)) / (h(x))^2
In this case, g(x) = 1 and h(x) = cos x.
Now let’s find the derivatives of g(x) and h(x):
g'(x) = 0 (since g(x) = 1, and the derivative of a constant is 0)
h'(x) = -sin x (derivative of cos x is -sin x)
Using the quotient rule, we can write the derivative of sec x as:
(sec x)’ = (0 * cos x – 1 * (-sin x)) / (cos x)^2
Simplifying this expression further:
(sec x)’ = sin x / (cos x)^2
Therefore, the derivative of sec x with respect to x is sin x / (cos x)^2.
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