d/dx secx
To find the derivative of sec(x), we can use the quotient rule
To find the derivative of sec(x), we can use the quotient rule. The quotient rule states that if we have a function f(x) = g(x)/h(x), then its derivative f'(x) can be found using the following formula:
f'(x) = (g'(x) * h(x) – g(x) * h'(x)) / [h(x)]^2.
In this case, we can represent sec(x) as 1/cos(x), which means g(x) = 1 and h(x) = cos(x).
Now let’s find the derivatives of g(x) and h(x):
g'(x) = 0 (since the derivative of a constant is always zero)
h'(x) = -sin(x) (using the derivative of cosine function, which is -sin(x))
Using the quotient rule, we can substitute the values of g'(x), g(x), h'(x), and h(x):
f'(x) = (0 * cos(x) – 1 * (-sin(x))) / [cos(x)]^2
Simplifying this equation gives us:
f'(x) = sin(x) / [cos(x)]^2
So, the derivative of sec(x) is sin(x) / [cos(x)]^2.
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