Suppose w=xy+yzw=xy+yz, where x=e2t, y=2+sin(4t)x=e2t, y=2+sin⁡(4t), and z=2+cos(5t)z=2+cos⁡(5t). a. use the chain rule to find dwdtdwdt as a function of x, y, z, and t. do not rewrite x, y, and z in terms of t, and do not rewrite e2te2t as x.

The chain rule is one of the techniques to take the derivative of an expression.

The value of the differentiation is:

The given parameters are:

Expand

Differentiate w with respect to t using chain rule.

So, we have:

Differentiate x, y and z with respect to t

Substitute these values in the equation of w'

Hence,

Read more about chain rule at:

link

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x