00:02
In this problem, we wish to find the derivative, d, y, dx for the function y is equal to 2x minus 5 to the 4th times 8x squared minus 5.
00:11
This question challenges our understanding of differentiation, in particular, it's challenging our knowledge of the short cut known as the derivative chain rule.
00:19
This rule states that for y equals f of u, dydx is dy to u or df to u times du d udx.
00:25
We combine the chain rule in conjunction with previously learned differentiation techniques like the quotient rule and power rule to solve.
00:31
In this problem, we're going to have a chain rule with this first term, 2x minus 5 to the 4th, where we use the product rule to differentiate when multiplied by this quantity on the right.
00:40
So, by the chain rule for our first term, f of u is u to the fourth, u is 2x minus 5, that's in parentheses, thus, d, d, y, to u, cubed, and d udx is 2...