How do you find the derivatives of #y=(2x+1)^e# by logarithmic differentiation?
1 Answer
Mar 8, 2017
Explanation:
Take the natural log of both sides.
#lny = ln(2x + 1)^e#
#lny = eln(2x + 1)#
Now use implicit differentiation and the product rule.
#1/y(dy/dx) = 0(ln(2x + 1)) + (2e)/(2x + 1)#
#dy/dx= y(2e/(2x + 1))#
#dy/dx = (2e(2x+ 1)^e)/(2x + 1)#
By the quotient rule of exponents:
#dy/dx = 2e(2x + 1)^(e - 1)#
Hopefully this helps!
