Show d/dx (cot x)=-(cosec x)^2.?
2 Answers
Mar 5, 2018
See explanation
Explanation:
We want find the derivative of
y=cot(x)=cos(x)/sin(x)
Use the quotient rule, if
then
f=cos(x)=>f'=-sin(x) g=sin(x)=>g'=cos(x)
Thus
Or
Mar 5, 2018
Explanation:
"differentiate using the "color(blue)"quotient rule"
"given "f(x)=(g(x))/(h(x))" then"
f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larrcolor(blue)"quotient rule"
f(x)=cotx=cosx/sinx
g(x)=cosxrArrg'(x)=-sinx
h(x)=sinxrArrh'(x)=cosx
rArrd/dx(cotx)
=(-sin^2x-cos^2x)/(sin^2x)
=(-(sin^2x+cos^2x))/sin^2x
=-1/sin^2x=-csc^2x