Use the given substitution and the chain rule to find
dy/dx
y=cos (6x - 5), u = 6x-5

Substituting u = 6x - 5, you write

y = cos(u)

Then differentiating with the chain rule gives

dy/dx = dy/du • du/dx

We have

dy/du = -sin(u)

du/dx = 6

so

dy/dx = -6 sin(u) = -6 sin(6x - 5)

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

the slope of the line is 60

one point on the line is (40,10)

step-by-step explanation:

in the equation outside the parenthesis the equation always tells you the slope. in this case it is 60.

in the parenthesis is also says 40 which is x because it is near the x and 10 is y because it is near y.