I'll explain how to do the first one:-
y = cos-1(x2)
This can be described as ' a function of a function' x^2 is a function of x and cos-1(x^2) is a function of x^2.
We need to apply the chain rule.
Personally I find this easier to understand if i let u = x^2, so
If y = f(u) and u is a function of x then
dy/dx = dy/ du * du/dx
Here u = x^2 and y = cos-1(u)
du/dx = 2x
so dy/dx = d(cos-1(x^2) dx = dy/du * du/dx
= -1 / √(1 - u^2) * 2x
= -2x / √(1 - u^2)
= -2x / √(1 - (x^2)^2)
= -2x / √(1 - x^4)
I hope this helps. but if not. you might like to employ the formulae in the question - The square boxes contain the 'u' s in my answer. These formulae are equivalent to my explanation.
The slope of the line that passes through points ( -10, -8 ) and ( -8, -16 ) is -4.
<u>Explanation:</u>
Points given = ( -10, -8) and ( -8, -16)
Slope = ?
( -10, -8 ) : x1 = -10 and y1 = -8
( -8, -16 ) : x2 = -8 and y2 = -16
We know,
slope = y2 - y1 / x2 - x1
Slope = -16 - ( -8) / -8 - (-10)
slope = -16 + 8 / -8 + 10
slope = -8 / 2
slope = -4
Therefore, slope of the line that passes through points ( -10, -8 ) and ( -8, -16 ) is -4.
The answer for 4 is 12..
hope it helps u..
have a great day ahead! :)
1.) 6x=12
x=2
3(2)+3y=-9
6+3y=-9
3y=-3
y=-1
(2,-1)
2.) 7x=-35
x=-5
5x+2y=-19
5(-5)+2y=-19
-25+2y=-19
2y=-44
y=-22
(-5,-22)
3.) 4x=-16
x=-4
2(-4) +3y=1
-8+3y=1
3y=-7
y=-7/3
(-4,7/3)
4.)7x=35
x=5
2(5)+3y=-5
10+3y=-5
3y=5
y=5/3
(5,5/3)
5.) 2x=-8
x=-4
x+4y=4
-4+4y=4
4y=0
y=1
(-4,1)
