Suppose that a duck is swimming in the circle x = cos(t), y = sin(t) and that the water temperature is given by the formula t = 5x2ey − 6xy3. find dt dt , the rate of change in temperature the duck might feel, by the following methods. (a) by the chain rule (b) by expressing t in terms of t and differentiating

Step-by-step explanation:

(a) By chain rule:

We can first use product rule to split up

From here apply chain rule for dx/dt and dy/dt we get

(b) by expressing T in term of t, we can substitute t for x and y in T

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right

c: y > - 1/6x + 1

step-by-step explanation:

dashed line - meaning this < or > also not equal

solid line - meaning this < or > also equal

your answer is c because y > means up & it's shaded up, but y < means down

hope this ! : )