How do you differentiate #f(x)=x/cotsqrtx# using the chain rule?

1 Answer

Answer:

#color(red)(f' (x)=(2sqrtx*cot sqrt(x)+xcsc^2 sqrt(x))/(2sqrtx*cot^2 sqrt(x)))#

Explanation:

From the given #f(x)=x/(cot sqrt(x))#

Use the Quotient Formula for finding derivatives

#d/dx(u/v)=(v*d/dx(u)-u*d/dx(v))/v^2#

Let #u=x# and #v=cot sqrt(x)#

#f' (x)=d/dx(x/cot sqrt(x))=(cot sqrt(x)*d/dx(x)-x*d/dx(cot sqrt(x)))/(cot sqrt(x))^2#

#f' (x)=(cot sqrt(x)+xcsc^2 sqrt(x)*1/(2sqrt(x)))/(cot sqrt(x))^2#

#color(red)(f' (x)=(2sqrtx*cot sqrt(x)+xcsc^2 sqrt(x))/(2sqrtx*cot^2 sqrt(x)))#

God bless....I hope the explanation is useful.