+209
y=x2/3+4
Find y' using implicit differentiation. Can someone please explain (Thoroughly) HOW to get the answer? I understand the concept but can't seem to apply it for the life of me.
Thanks in advance.
Find the derivative of the following via implicit differentiation:
d/dx(y) = d/dx(4+x^2/3)
The derivative of y is y'(x):
y'(x) = d/dx(4+x^2/3)
Differentiate the sum term by term and factor out constants:
y'(x) = d/dx(4)+(d/dx(x^2))/3
The derivative of 4 is zero:
y'(x) = 1/3 (d/dx(x^2))+0
Simplify the expression:
y'(x) = 1/3 (d/dx(x^2))
Use the power rule, d/dx(x^n) = n x^(n-1), where n = 2: d/dx(x^2) = 2 x:
y'(x) = 1/32 x
Expand the left hand side:
Answer: | y'(x) = (2 x)/3
