Assume that f is a de ferentiable function with fax (5,0) =6 and fu(5, )=4. Let w Cu,v) =f (x (u,v), y (u,v)) where x=6 cos(u) + 5 sin (V) and y= 7cos (u)sin(v)· Your Job is to find Wu (T/2, T/2).

Q: Find f. f ''(t) = 3et + 6 sin t, f(0) = 0, f(?) = 0 f(t)=

A: Solution

Q: Find f. f ''(θ) = sin(θ) + cos(θ),    f(0) = 5,    f '(0) = 1

A: given, f ''(θ) = sin(θ) + cos(θ),    f(0) = 5,    f '(0) = 1 to find f.

Q: 2. Find the directional derivative of f(x,y) = x cos y in the direction of v = 22, -1). A. (2 cos y…

A:

Q: Find the directional derivative of the function at the point P(2,1) in the following direction:…

A: The given function is:f(x,y)=3x2y-2xy2+y3-9P=(2, 1)Direction vector:  v=3i-5j

Q: Suppose y is a function of x. Find y' given csc-1y + xy = sec 1 y.

A: Given, csc-1y+xy=sec-1y

Q: find the first and the second derivative of these equation , first as a function of z then as a…

A: Given: Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: Find f. f"(θ)  = Sin θ  +Cos θ , f(0)  =3 , f'(0)  =4

A: Given functionf"(θ)  = Sin θ  +Cos θ , f(0)  =3 , f'(0)  =4we have to find , f(θ)

Q: Let f(x,y)=tan^-1(y,x). Find and simplify fx and fy. Then find and simplify fxx, fxy, and fyy.

A:

Q: Find f. f ''(t) = 4et + 6 sin t,    f(0) = 0,    f(?) = 0

A: To find f. f''(t)=4et+6sint,f(0)=0,f'(0)=0

Q: 3. Find the derivative of y with respect to x in the followin u? a) у3 u = 3x' - 2 and u' + 1 b)…

A:

Q: Determine the two-variable function F(x, y) if Fy (x, y) = y sin(xy) + x given that x^2 + πχ2 F(x₁ -…

A: Given That: Partial derivative of a function with respect to y is Fy(x,y)=ysin(πxy)+x with the…

Q: Find y as a function of a if y(1) = 8, y'(1) = 6. y = x²y" + 3xy' - 35y = 0,

A:

Q: Find the derivative (dy/dx) of the following functions: h) у%3D Зx7 —7х3 + 21x2 - i) y = (x² +…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: Write the function f(x,y) = xcosh(x)cos(y) - ysinh(x)sin(y) + i(xsinh(x)sin(y) + ycosh(x)sin(y)) in…

A: f(z)=Re(z)cosh(Re(z))cos(Im(z))−Im(z)sinh(Re(z))sin(Im(z))+i(Re(z)sinh(Re(z))sin(Im(z))+Im(z)cosh(Re…

Q: Define f = sin(px^3)+cos(qx)^2 as a function of x (with p and q constant) and differentiate with…

A: see 2nd step.

Q: 3 Ay 10- Find equation of tangent line at the point (0, 7) for Cos (7x - y)

A: Solving

Q: 2. (5) Find f, for the function f(x, y) = sin (x + y²)

A:

Q: Find the directional derivative of the function at the point P in the direction of the point . f(x,…

A: