Could you please give me some guidance on these problems? I have been stuck with these problems for a while today.

Thank you for your help in advance!

15.4.61 Consider the surface 2 = f(x,y) : 3x2 + 4y2 +1 and the curve C in the xyeplane given parametrically as x : cost and y: sin t where D St 321:. a. Find z'(t). b. Imagine that you are walking on the surface directly above the curve C in the direction of positive orientation. Find the values oft for which you are walking uphill (that is, z is increasi a. Find the intermediate derivatives. 32 a): (Type an expression using x and y as the variables.) Enter your answer in the answer box and then click Check Answer. 5 9333mm I ' CIearAII 15.4.51-Setup & Solve Find the derivative dw at : where w = xyz, x = 214, y = 3t -1, and z = 5t - 3 ow ox Type an expression using x, y, and z as the variables.) Enter your answer in the answer box and then click Check Answer. 6 parts remaining Clear All15.4.29 1 1 Find z'(t), where z 2 E + g x :t2 + 3t, and y :t3 4, in the following ways. a. Replace x and y to wte I as a function of t and differentiate, In. Use the Chain Rule. a. Write 2 as a function of l. Z(t) : Enter your answer in the answer box and then click Check Answer. pans 5 remaining - Clear All 15.4.40-Setup & Solve Given the equation y In (x3 + y2 + 4) =3, evaluate dx Assume that the equation implicitly defines y as a differentiable function of x. If F(x,y) = yIn (x3 + y2 + 4) -3, then Fx =]. Enter your answer in the answer box and then click Check Answer. parts Clear All15.4.39-Setup & Solve Given the equation 1 x2 + 4xy + y# =2, evaluate . Assume that the equation implicitly defines y as a differentiable function of x. If F(x,y) = 1x2 + 4xy +y4 - 2=0, then Fx = Enter your answer in the answer box and then click Check Answer. 2 parts remaining Clear All