Taking the derivative of 7 times secant of x^3:
We take out 7 as a constant focus on secant (x^3)
To take the derivative, we use the chain rule, taking the derivative of the inside, bringing it out, and then the derivative of the original function. For example:
The derivative of x^3 is 3x^2, and the derivative of secant is tan(x) and sec(x).
Knowing this: secant (x^3) becomes tan(x^3) * sec(x^3) * 3x^2. We transform tan(x^3) into sin(x^3)/cos(x^3) since tan(x) = sin(x)/cos(x). Then secant(x^3) becomes 1/cos(x^3) since the secant is the reciprocal of the cosine.
We then multiply everything together to simplify:
sin(x^3) * 3x^2/ cos(x^3) * cos(x^3) becomes
3x^2 * sin(x^3)/(cos(x^3))^2
and multiplying the constant 7 from the beginning:
7 * 3x^2 = 21x^2, so...
our derivative is 21x^2 * sin(x^3)/(cos(x^3))^2
It has two pairs of same angles: that means that the opposite sides are parallel: this makes it a parallelogram.
Answer:
I can't answer that if there is no picture, I'm sorry
In quotient your answer would be 70
Answer:
The slope is 2/3 and the function is y=2/3x which is a direct variation function.
Step-by-step explanation:
To find the slope of a line between two points, we use the equation
m = (y2-y1)/ (x2-x1)
where (x1,y1) and (x2,y2) are the two points
m= (4-2)/(6-3)
= 2/3
The slope of the line is 2/3
The equation of the line is
y-y1 = m(x-x1)
y-2 = 2/3(x-3)
Distribute
y-2 = 2/3x -2
Add 2 to each side
y-2+2 = 2/3x -2+2
y = 2/3x
This is a direct variation function
Let x = -6
y = 2/3(-6)
y = -4
(-6,-4)
