d/dx secx
To find the derivative of sec(x), we can use the quotient rule of differentiation
To find the derivative of sec(x), we can use the quotient rule of differentiation. The formula for the quotient rule states that if you have a function f(x) = g(x)/h(x), then the derivative of f(x) can be found using the following formula:
f'(x) = (g'(x) * h(x) – g(x) * h'(x)) / (h(x))^2
For the function f(x) = sec(x), we can express it as f(x) = 1/cos(x).
Therefore, g(x) = 1 and h(x) = cos(x).
To find g'(x) and h'(x), we need to differentiate the functions g(x) and h(x) separately.
Differentiating g(x):
g'(x) = 0 (since g(x) = 1, which is a constant)
Differentiating h(x):
h'(x) = -sin(x) (since the derivative of cos(x) is -sin(x))
Now, we can substitute the values into the quotient rule formula:
f'(x) = (g'(x) * h(x) – g(x) * h'(x)) / (h(x))^2
= (0 * cos(x) – 1 * -sin(x)) / (cos(x))^2
= sin(x) / (cos(x))^2
Therefore, the derivative of sec(x) is sin(x) / (cos(x))^2.
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