How do we determine the derivative of #y = log_10sqrt(x^2 + 3x +4)#?
1 Answer
Dec 12, 2016
#y = logsqrt(x^2 + 3x + 4)#
#y = 1/2log(x^2 + 3x + 4)#
#2y = log(x^2 + 3x + 4)#
#10^(2y) = x^2 + 3x + 4#
#ln(10^(2y)) = ln(x^2 + 3x + 4)#
#(2y)ln10 = ln(x^2 + 3x + 4)#
Use the chain rule to differentiate the right hand side and the product rule to differentiate the left hand side.
#2(dy/dx)ln10 + 2y(0) = 1/(x^2 + 3x + 4) xx 2x + 3#
#2ln10(dy/dx) = (2x+ 3)/((x + 3)(x + 1))#
#dy/dx = (2x + 3)/(ln100(x+ 3)(x + 1))#
Hopefully this helps!
