![]() ![]() On top, which is zero, times the expression on theīottom, which is sine of x. So it's going to be the derivative of the expression Once again, we'll do the quotient rule, but you could also do Cosine's reciprocal isn'tĬosecant, it is secant. Thing as the derivative with respect to x of one over sine of x. Of secant of x is sine of x over cosine-squared of x. And of course this is tangent of x, times secant of x. Is same thing as sine of x over cosine of x times And so all we are left with is sine of x over cosine of x squared. And so zero times cosine of x, that is just zero. And then all of that over the function on the bottom squared. It'll be a negative, so we can just make that a positive. But it's negative sine of x, so you have a minus and Well, the derivative on the bottom is, the derivative of cosine Of one with respect to x? Well, that's just zero. Going to be equal to, it's going to be equal to The quotient rule actually can be derived based on the chain ruleĪnd the product rule. But we know the quotient rule, so we will apply the quotient rule here. More natural thing to use to evaluate the derivative here. When you learn the chain rule, that actually might be a And that's just the definition of secant. Well, secant of x is the same thing as so we're going to find theĭerivative with respect to x of secant of x is the same thing as one over, one over the cosine of x. This video is to keep going and find the derivatives of ![]() Video we used the quotient rule in order to find the derivatives of tangent of x and cotangnet of x. ![]()
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