00:01
Hi, today we will be solving the following problem.
00:04
Find the derivative of w of y, which is defined as 6 times y to the power of 4 plus 7 times y to the power of 2 thirds.
00:14
Now to solve this problem, let's review the power rule of taking derivatives.
00:19
That is, if you want to take the derivative of function, and i can signify them taking the derivative with respect to x by saying d d dx of a function x to the power 5, the derivative of x to the power of i is going to be i times x to the power of i minus 1.
00:43
Now if we have a constant before x any value, so we can write that out by saying the derivative, or d dx, of some constant c times x to the power of i, and note that x is a variable while i and c are with constant numbers.
01:06
The derivative of that would be c times d, d, x, or the derivative with respect to x, of x to the power of i.
01:23
And this is because the value of c is constant, so it doesn't change with x.
01:27
So you can just move it outside of the derivative.
01:32
And that would be equal to c times i times x to the power of, i minus one now we can use these principles to solve for the derivative of w of y now in my examples i use the variable x but since we're taking the derivative with respect to y the principle is the exact same thing but was just different and it was a different name for the variable so let's get rid of all this stuff over here and start solving for our derivative of w of y okay, so we have the w of y is equal to six times y to the power of four plus seven times y to the power of two thirds...