d sec(x)
The expression d sec(x) represents the derivative of the secant function with respect to x
The expression d sec(x) represents the derivative of the secant function with respect to x. In order to find this derivative, we can use the quotient rule.
The secant function, sec(x), can be written as 1/cos(x). Using the quotient rule, we have:
d(sec(x))/dx = (1)(d/dx(cos(x))) – (cos(x))(d/dx(1))
To find the derivative of cosine function, d/dx(cos(x)), we can use the chain rule, which states that the derivative of a composite function is equal to the derivative of the outer function times the derivative of the inner function.
The derivative of cosine function is -sin(x). Therefore, substituting this in the equation, we get:
d(sec(x))/dx = (1)(-sin(x)) – (cos(x))(0)
Since the derivative of a constant function such as 1 is 0, the second term in the equation becomes 0.
Simplifying the equation, we finally have:
d(sec(x))/dx = -sin(x)
Hence, the derivative of the secant function with respect to x is equal to the negative sine of x, d(sec(x))/dx = -sin(x).
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