Derivative of sec x
The derivative of sec x can be found using the chain rule
The derivative of sec x can be found using the chain rule.
Recall that the chain rule states that if we have a composite function y = f(g(x)), then the derivative of y with respect to x is given by:
dy/dx = (df/dg) * (dg/dx)
In this case, we can rewrite sec x as 1/cos x. So we have:
y = sec x = 1/cos x
Let’s use the chain rule to find the derivative of sec x.
First, we need to find df/dg, where f(g) = 1/g.
df/dg = -1/g^2
Next, we need to find dg/dx, where g(x) = cos x.
dg/dx = -sin x
Now, we can multiply these two derivatives together to find the derivative of sec x:
dy/dx = (df/dg) * (dg/dx) = (-1/g^2) * (-sin x) = sin x / (cos^2 x)
Therefore, the derivative of sec x is sin x / (cos^2 x).
To summarize, the derivative of sec x is sin x / (cos^2 x).
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