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,  

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

fa tha first one you gonna add y to both sides

it look like this

x-y+y=6+y

x=y+6

therefore your answer is

x =y+6

fa tha second one

you gonna flip tha equation

it gonna look like x-4y=y

then add 4 to both sides

it gonna look like tha

x-4 +4 =y +4

so therefore tha answer is x=y+4

step-by-step explanation: