Quotient Rule
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How to differentiate tanx using the quotient rule
by
Tiago Hands
Key Questions

#y'=(g(x)f'(x)f(x)g'(x))/(g(x))^2# #y=f(x)/g(x)=(2x^43x)/(4x1)# #f'(x)=8x^33# #g'(x)=4# #(g(x))^2=(4x1)^2# #y'=((4x1)(8x^33)(2x^43x)(4))/(4x1)^2# #y'=(32x^412x8x^3+38x^4+12x)/(4x1)^2# Simplify for combining like terms.
#Solution>y'=(24x^48x^3+3)/(4x1)^2# 
#y'=1/(sqrtx)*1/((1sqrtx)^2)# Explanation :
Using Quotient Rule, which is
#y=f(x)/g(x)# , then#y'=(g(x)f'(x)f(x)g'(x))/(g(x))^2# Similarly following for the given problem,
#y=(1+sqrtx)/(1sqrtx)# #y'=((1sqrtx)(1/(2sqrtx))(1+sqrtx)(1/(2sqrtx)))/((1sqrtx)^2)# #y'=1/(2sqrtx)*(1sqrtx+1+sqrtx)/((1sqrtx)^2)# #y'=1/(2sqrtx)*(2)/((1sqrtx)^2)# #y'=1/(sqrtx)*1/((1sqrtx)^2)# 
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