d/dx secx
To find the derivative of sec(x) with respect to x, we can use the quotient rule
To find the derivative of sec(x) with respect to x, we can use the quotient rule. The quotient rule states that if we have a function of the form f(x) = g(x)/h(x), the derivative of f(x) is given by:
f'(x) = (g'(x) * h(x) – g(x) * h'(x))/[h(x)]^2
Applying the quotient rule to sec(x), which can be written as 1/cos(x), we can let 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 0.
h'(x) = -sin(x), as the derivative of cos(x) is -sin(x).
Now, we can substitute these values into the quotient rule formula:
f'(x) = (0 * cos(x) – 1 * (-sin(x)))/[cos(x)]^2
Simplifying further:
f'(x) = sin(x)/[cos(x)]^2
Therefore, the derivative of sec(x) is equal to sin(x)/[cos(x)]^2.
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