derivative of secx
derivative of secx is -tanx * secx.
The derivative of secx can be found using the quotient rule and the chain rule. Recall that secx is defined as 1/cosx. Thus,
d/dx(secx) = d/dx(1/cosx)
Using the quotient rule, we have:
= (cosx*d/dx(1) – 1*d/dx(cosx))/(cosx)^2
Since the derivative of a constant is zero, we can simplify this expression to:
= (-sinx)/(cosx)^2
Next, we can simplify this expression using the identity sin^2x + cos^2x = 1. Rearranging, we have sin^2x = 1 – cos^2x. Thus, we can substitute (1 – cos^2x) for sin^2x in our expression:
= -1/(cosx)^2 * (1 – cos^2x)/(1)
Simplifying further, we get:
= -tanx * secx
Therefore, the derivative of secx is -tanx * secx.
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