How to Find the Derivative of secx with Respect to x Using the Quotient Rule

(d/dx) secx

The notation (d/dx) represents the derivative with respect to x

The notation (d/dx) represents the derivative with respect to x. So, (d/dx) secx means the derivative of secx with respect to x.

To find the derivative of secx, we can use the quotient rule. The quotient rule states that if we have a function of the form f(x) = g(x)/h(x), then the derivative is given by:

f'(x) = (g'(x) * h(x) – g(x) * h'(x)) / (h(x))^2

In this case, g(x) = 1 and h(x) = cosx, because secx is equal to 1/cosx.

So, let’s differentiate g(x) and h(x) individually:

g'(x) = 0 (the derivative of a constant is zero)

h'(x) = -sinx (using the derivative of cosx, which is -sinx)

Now, we can substitute these values into the quotient rule formula:

f'(x) = (0 * cosx – 1 * (-sinx)) / (cosx)^2

Simplifying, we have:

f'(x) = sinx / (cosx)^2

Therefore, the derivative of secx with respect to x is sinx / (cosx)^2.

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