Find dy du , du dx , and dy dx .

(a) y = u5 and u = x2 + 1 dy du = du dx = dy dx =

(b) y = u4 and u = 4x2 − x + 6 dy du = du dx = dy dx =

a) , ,  

b) , ,  

Step-by-step explanation:

We can use the chain rule in the following form: is u=u(x) is a differentiable function depending on x and y=y(u) is a differentiable function depending on u, then .

a) from the power rule.  

.

From the previous parts and the chain rule,  

b)  

from the power and sum rules.

Then,  

y < -3

step-by-step explanation:

-3y - 2 > 7

-3y -2 + 2 > 7+2

-3y > 9

-3y/-3 < 9/-3   (change the inequality sign when multiplying or dividing by a negative number)

y < -3