find the derivative of f(x)= (cotx)/(sinx) and SHOW WORK.?

the answer given in the back of the textbook is (-1-cos^(2)x)/(sin^(3)x). i need to see the work shown to acquire this answer. we were taught to use the chain rule, but i have no idea how to apply the chain rule to this problem and solve it.

thanks 🙂

Top 1 Answers

A few days ago

Anonymous

Favorite Answer

You need the quotient rule (not the chain rule) to differentiate this. The quotient rule is:

(d/dx)(u / v) = (v du/dx – u dv/dx) / v^2.

Applying it to this quotient gives:

f'(x) = ( sin(x) (-cosec^2(x)) – cot(x)cos(x) ) / sin^2(x)

= [ – 1 / sin(x) – cos^2(x) ] / sin^2(x)

= [ – 1 – sin(x)cos^2(x) ] / sin^3(x).

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find the derivative of f(x)= (cotx)/(sinx) and SHOW WORK.?

find the derivative of f(x)= (cotx)/(sinx) and SHOW WORK.?

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