Derivitive of sec(x)
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. However, it is more convenient to derive it from the identity sec(x) = 1/cos(x).
Let’s start by finding the derivative of cos(x). We know that the derivative of cos(x) is -sin(x).
Now, using the quotient rule, we can find the derivative of sec(x):
d/dx [sec(x)] = d/dx [1/cos(x)]
= [0 * cos(x) – 1 * (-sin(x))] / (cos(x))^2
= sin(x) / (cos(x))^2
= sin(x) / cos^2(x)
= sin(x) * (1/cos^2(x))
= sin(x)/cos^2(x)
Recall that sin(x) / cos^2(x) is the same as sec(x) * tan(x).
Therefore, the derivative of sec(x) is sec(x) * tan(x).
In summary, the derivative of sec(x) is sec(x) * tan(x).
More Answers:
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