00:01
Hi, thank you so much for your question.
00:02
Find derivative of each function.
00:04
Okay, first for a we have f of x equals 13 times x to the fourth power minus 7 times x cubed plus 5 times x squared plus 11x plus 75.
00:19
Okay, so f prime of x would be 52 times x cubed minus 21 x squared plus 10x plus 11.
00:44
11.
00:45
Okay? so now let's look at second one, look at b.
00:53
F of x is f cubed plus 2x squared plus 4 times x to the fourth power minus 3.
01:04
Okay? so we have f prime of x equals, let's find derivative of first bracket first.
01:12
So 3x squared plus 4x times x to the fourth power minus 3 plus x cubed plus 2x squared plus 4 times take the derivative of the second bracket so 4x okay you can simplify it but i will just leave as it is okay you can simplify by yourself now see okay f of x equals 3x squared minus minus 6x plus 7 over 4x minus 1.
01:56
Okay? so derivative denominator is a square of 4x minus 1.
02:18
And the numerator is, take the derivative of the numerator and times the denominator minus the numerator times the derivative of the denominator.
02:33
Okay? again, you can simplify it by itself, but i will leave just as it is, okay? and because we have so many questions, right? now let's look at d.
02:47
F of x is 4x cubed minus 7x to the 7th power.
02:53
Okay, let's find derivative.
02:55
So derivative is 7 times 4x cubed minus 7x to the 6th power times 12x squared minus 7, okay? it's just very easy.
03:15
You just need to apply the formula.
03:16
If you don't know how to solve this, that means you're not familiar with the formulas.
03:21
Just go back and check the derivative formula sheet and apply each one with corresponding formula.
03:31
This one has implicit differentiation.
03:34
Differentiation.
03:34
So right side, left side is 0.
03:37
Right side is 3y squared times y prime with respect to x and plus 2x.
03:46
If you want to find y prime, y prime would be, okay, negative 2x over 3y squared, and let's look at f.
04:04
F, we have f of x is 156.
04:13
So what is f prime? f prime of x is 0.
04:21
And g, f of x is 1 minus 3x squared times x squared minus 2 cube.
04:34
So let's find f '.
04:41
F ' is, take the derivative of the first bracket, and then multiply the second bracket, and we add the first bracket, multiply the derivative of the second bracket, then we got this...