d/dx(secx)
To find the derivative of the secant function, we can use the quotient rule
To find the derivative of the secant function, we can use the quotient rule. Recall that the secant function can also be written as 1/cos(x). Applying the quotient rule, we have:
d/dx(secx) = d/dx(1/cosx)
= (cosx * d/dx(1) – 1 * d/dx(cosx)) / (cosx)^2
Now let’s find the derivatives on the top of the expression:
d/dx(1) = 0 (the derivative of a constant is always zero)
d/dx(cosx) = -sinx (using the derivative of the cosine function)
Substituting these derivatives into our expression, we have:
= (cosx * 0 – 1 * (-sinx)) / (cosx)^2
= sinx / (cosx)^2
This is the derivative of the secant function, which can also be written as tanx * secx.
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