Advanced Derivatives Derivative of ln Find the derivative of the following function: Chain Rule Define a function u = x + 2 4x Find the derivative of u = dx du 2x +4
This is what we have so far......... y = ln(x + 2 4x) = dx du 2x +4 Let's find the derivative of y dx dy = dx dy x +4x 2 1 dx du Since the derivative of ln is: ln(x) = dx dy x 1 = dx dy (2x + x +4x 2 1 4)
FIND THE DERIVATIVE OF LOG y = log (3x − 4 3 8x )2
what is the derivative of the log function? y = log xa = dx dy xlna 1 Apply the chain rule Make u = 3x − 3 8x2 Find dx du = dx du 9x − 2 16x
First,
y = log (3x − 4 3 8x )2 u = 3x − 3 8x2 = dx du 9x − 2 16x Substitution = dx dy uln(a) 1 dx du = dx dy (9x − (3x −8x )ln4 3 2 1 2 16x)