(14 points) Let f: R3 R and T: R3. →R³ be defined by f(x, y, z) = ln(x²+ y²+2²), T(p, 0,4)=(psin cos 0, psin sin, pcos). (a) (4 points) Write out the composition g(p, 0, 4) = (foT)(p,, ) explicitly. Then calculate the gradient Vg directly, i.e. without using the chain rule. (b) (4 points) Calculate the gradient Vf(x, y, z) where (x, y, z) = T(p, 0,4). (c) (6 points) Calculate the derivative matrix DT(p, 0, p). Then use the Chain Rule to calculate Vg(r,0,4).

Let F = (cos(5t), sin(3t) , 5t“) and G = (t cos(5t), cos(5t), Find F +G = (5t^4)+sin(3t)+t^4(cos(5t))+5e^4t

Can someone help me with this please?

FCx): 2x-5xナ3 find f'co).

9 To express Q(x) = cos(4x-5) as the composition of three functions, identify f, g, and h so that Q(x) = f(g(h(x))). CTTH) Which functions f, g, and h below are correct? O A. OB. h(x)=4x-5 h(x)=4x-5 g(x) = cos(x) f(x)=x g(x)=x⁹ f(x) = cos(x) - 5 O C. h(x) = cos (x) - 5 OD. h(x) = 4x g(x)=x g(x) = cos(x) - 5 f(x)=x² f(x) = 4x O E. h(x) = 4x-5 OF. h(x) = cos (x) g(x)=x g(x)=x f(x) = cos(x) f(x) = 4x-5

Integrate the trig identity 2 cos j x cos kx = cos(j + k )x + cos(j -k )x to show that cos j x is orthogonal to cos kx, provided j -/- k. What is the result when j = k?

B) Find- for following functions: дz əs 1) z = exy tan y, x = s + 2t, y = s/t. 2) z = x² + xy + y², x = s+t, y = st.

2, y = 2 + cos x