00:01
In this problem, we are asked to find the derivative of the function, h of x equals x square minus 1 whole cubed.
00:10
Now i'm going to use the expansion formula for a minus b, whole cube is a cubed minus b cubed minus b cubed minus 3 a square b plus 3 a b square b.
00:28
So here my a is x square and b is negative b is 1 so using the expansion formula i get x squared minus 1 cubed minus 3 x squared squared times 1 plus 3 x square times 1 square so that becomes x raised to the x square raised to the 3 is x to the 6 minus 1 minus 3 x to the 4th plus 3x square now the derivative of a sum or difference of functions is same as the sum or difference of its derivatives so d, d, d x of h of x is going to equal to d dx of x to the 6th, minus d d dx of 1, minus d d dx of 3x to the 4th, plus ddx of 3x square.
01:49
In these two cases, 3 is a constant, so we can pull that out of the derivative.
01:56
1 is a constant so this derivative is 0.
02:01
Now we can use the power rule to find the other derivatives.
02:06
Now the power rule states that ddx of x raise to the n is n times x raised to the n minus 1.
02:16
So these are our ns.
02:20
So the derivative of x raise to the 6 is 6 times x raised to the 6 minus 1.
02:26
That derivative is 0...