Question 993255: Suppose ln (x + 2y) = x^4.
Use implicit differentiation to find the derivative of y with respect to x
Thank you Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website! d/dy(ln(x+2y))= d/dy(x^4)
Chain rule: d/dy(log(x+2y)) = (dlog(u))/(du)(du)/(dy), where u= x+2y and (d)/(du)(log(u))= 1/u:
(d/dy(x+2y))/(x+2y)= d/dy(x^4)
Differentiate the sum term by term and factor out constants:
d/dy(x)+2d/dy(y)/(x+2y)= d/dy(x^4)
The derivative of x is zero:
(2(d/dy(y))+0)/(x+2 y)= d/dy(x^4)
Simplify the expression:
(2(d/dy(y)))/(x+2y)= d/dy(x^4)
The derivative of y is 1:
((1)(2))/(x+2 y)= d/dy(x^4)
The derivative of x^4 is zero:
2/(x+2 y)= 0
