Differentiate cosx/sinx ? (1 Viewer)

[eels_no1]

I use the quotient rule but I get stuck, any help?

 

[Crisium]

cos (x) / sin (x)

u = cos (x) v = sin (x)

u' = -sin (x) v' = cos (x)

Quotient Rule:

(vu' - uv') / v^2

Sub in the values above and you should have the answer

 

[Crisium]

Wait I think I understand where you might be having troubles

If you sub it in then you get

-sin^2(x) - cos^2(x) / sin^2(x)

= - ( sin^2(x) + cos^2(x) ) / sin^2(x)

Using the identity sin^2(x) + cos^2(x) = 1

= - 1 / sin^2(x)

Using normal trig ratios

= - cosec^2(x)

 

[eels_no1]

Wait I think I understand where you might be having troubles

If you sub it in then you get

-sin^2(x) - cos^2(x) / sin^2(x)

= - ( sin^2(x) + cos^2(x) ) / sin^2(x)

Using the identity sin^2(x) + cos^2(x) = 1

= - 1 / sin^2(x)

Using normal trig ratios

= - cosec^2(x)

Perfect! I was stuck at the factorising bit, where you took out the negative. Thanks!