URGENT HELP NEEDED - PLEASE PROVIDE WRITTEN STEP BY STEP
(a) Find f_(x)(0,0) if f(x,y)=(e^(3+2y))/(3x+5).
(b) Given f(x,y)=e^(-2y)cos2x, show that f_(zx)+f_(yy)=0.
(c) Use the chain rule to calculate (delz)/(delu), given z(x,y)=e^(x^(2)y), where :
x(u,v)=sqrt(uv)
y(u,v)=(1)/(v)
Express your result in terms of u and v.
(d) Find the rate of change of the area of a rextangle in the instant when it is 60cm long
and 30cm wide, if the length decreases at a constant rate of 5c(m)/(s) and the width
increases at a constant rate of 8c(m)/(s).
(e) Find the minimum value of f(x,y)=2x+3y, subject to the constraint g(x,y)=
x^(2)+2y^(2)-34.
(f) Find the rate of change of f(x,y)=3x^(2)+2xy^(2) at (-1,3) measured in the direction
2i+j
e3+2y aFind f0,0if fy 3+5
[2]
(b) Given f(, y) = e2y cos 2, show that fzr + fyy = 0.
[2]
9z (c) Use the chain rule to caleulate :given ,y=ey,here : .n0
[2]
(,v) =/uv
yuv=
Express your result in terms of u and v
(d) Find the rate of change of the area of a rectangle in the instant when it is 60cm long and 30cm wide, if the length decreases at a constant rate of 5 cm/s and the width increases at a constant rate of 8 cin/s. [s]
(e) Find the minimum value of f(,y) = 2x + 3y. subject to the constraint g(x,y) = 2 + 2y2 34. [4]
(f) Find the rate of change of f(,y) = 32 + 2xy2 at (1,3) measured in the direction 2i+j [3]