d/dx(secx)
secxtanx
To find the derivative of sec(x) with respect to x, we need to use the chain rule and the fact that sec(x) is equal to 1/cos(x). That is:
d/dx(sec(x)) = d/dx(1/cos(x))
Now, let’s use the power rule and the chain rule to find the derivative. That is:
d/dx(1/cos(x)) = -1/cos^2(x) * d/dx(cos(x))
To find d/dx(cos(x)), we need to use the chain rule again. That is:
d/dx(cos(x)) = -sin(x)
Putting everything together, we get:
d/dx(sec(x)) = -1/cos^2(x) * (-sin(x)) = sin(x)/cos^2(x) = sin(x)sec^2(x)
Therefore, the derivative of sec(x) with respect to x is sin(x)sec^2(x).
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