How do you use the quotient rule to differentiate #(2lnx^3) / sqrt(2-x^2)#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer maganbhai P. Mar 18, 2018 #=>(dy)/(dx)=6[(2-x^2+x^2lnx)/(x(2-x^2)^(3/2))]# Explanation: Here, #2lnx^3=2(3lnx)=6lnx# So, let us take #y=(6lnx)/sqrt(2-x^2)# Now, #color(red)(d/(dx)(u/v)=(v*u^'-u*v^')/v^2)# #:.(dy)/(dx)=6[(sqrt(2-x^2)*1/x-lnx*1/(cancel(2)(sqrt(2-x^2)))(-cancel(2)x))/((sqrt(2-x^2))^2)]# #=6[(sqrt(2-x^2)/x+(xlnx)/(sqrt(2-x^2)))/(2-x^2)]# #=6[((2-x^2)+(x^2lnx))/(xsqrt(2-x^2)(2-x^2))]# #=>(dy)/(dx)=6[(2-x^2+x^2lnx)/(x(2-x^2)^(3/2))]# Answer link Related questions What is the Quotient Rule for derivatives? How do I use the quotient rule to find the derivative? How do you prove the quotient rule? How do you use the quotient rule to differentiate #y=(2x^4-3x)/(4x-1)#? How do you use the quotient rule to differentiate #y=cos(x)/ln(x)#? How do you use the quotient rule to find the derivative of #y=tan(x)# ? How do you use the quotient rule to find the derivative of #y=x/(x^2+1)# ? How do you use the quotient rule to find the derivative of #y=(e^x+1)/(e^x-1)# ? How do you use the quotient rule to find the derivative of #y=(x-sqrt(x))/(x^(1/3))# ? How do you use the quotient rule to find the derivative of #y=x/(3+e^x)# ? See all questions in Quotient Rule Impact of this question 1508 views around the world You can reuse this answer Creative Commons License