d/dx [secx]
To find the derivative of the secant function (secx) with respect to x, we can use the chain rule
To find the derivative of the secant function (secx) with respect to x, we can use the chain rule.
The chain rule states that if we have a composite function f(g(x)), then the derivative of that function with respect to x is given by the derivative of the outer function (f'(g(x))) multiplied by the derivative of the inner function (g'(x)).
In this case, the outer function is secx, and the inner function is x.
The derivative of the secant function is given by the derivative of its reciprocal, which is cosine (cosx). So, we have:
d/dx [secx] = d/dx [1/cosx]
To find the derivative of 1/cosx, we can use the quotient rule. The quotient rule states that if we have a function of the form f(x)/g(x), then its derivative is given by (g(x)f'(x) – f(x)g'(x))/[g(x)]^2.
In this case, f(x) = 1 and g(x) = cosx. Therefore, we have:
d/dx [1/cosx] = (cosx(0) – 1(-sinx))/[cosx]^2
Simplifying this expression, we have:
d/dx [1/cosx] = sinx/[cosx]^2
Therefore, the derivative of secx with respect to x is sinx/[cosx]^2.
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