00:01
Here we are asked to find out the derivative.
00:03
So for part a fx is given to us is 2x to the power 5 minus 5x cube.
00:12
You can refer to the image right.
00:15
So in image text is wrong right and image you can refer to plus 7x minus 8.
00:24
So since we know a rule for derivative d by dx of x to the power n is nothing but that would be nx to the power n minus 1 yes this is what we are going to use here so now f prime x or f dash x that is represented for that is a representation of derivative right it is equals to 2 multiplied by because 2 is a constant value and differentiation of x to the power 5 that would be 5x to the power 4.
01:02
Negative of 5 multiplied by because 5 is a constant value and differentiation of x cube only will do.
01:10
So that would be 5 multiplied by 3x square plus 7 because differentiation differentiation of x is going to be 1 itself.
01:20
And differentiation of 8 is 0 here.
01:25
So, let us just write this value.
01:26
This is 10x to the power 4 negative of 15x square plus 7.
01:35
So, this is going to be the derivative of it.
01:38
Right? this is going to be the answer for the first part.
01:41
Now, moving forward with the next part of this problem.
01:45
What we are given with? we are given with x cube plus 1.
01:57
Fx is equal to x cube plus 1 upon x cube minus 1.
02:08
Right? so what we know the formula since differentiation of when it is asked it is hx let us say hx upon gx.
02:23
This is the derivative it is asked.
02:26
So what is going to be the formula? the formula would be gx then differentiation of hx minus hx and differentiation of gx, right? so this this is whole divided by gx whole square.
02:55
This is going to be formula we are going to use here.
03:00
Yes...