Suppose: w = f (s,t) s = s (x, y) and s(1, 10) = –6 t =t(x, z) and t(1, –9) = 3 Ultimately, after substituting in the lower variables, w (x, y, z) will be a function of x, y, and z. Write down the Multivariable Chain Rule (assume everything is differentiable) formula for: Wz (1, 10, –9) = fs (???, ???)* s? (???, ???)+more terms! [Use Lagrange notation (the subscripts)!] Hint: Where do we evaluate each partial derivative?

Q: 3. Let f(x) = x² + 3 and g(x) = Vx – 3 be functions defined on [0, ∞) and [3, 00), respectively. i.…

A: According to question,  Given functions, f(x) = x2+3, g(x) = x-3 Function fx defined on interval :…

Q: The gradient of the function 2x1 + x2 - 3 evaluated in x = (0 0 0) is: OA. Vf=(1 2 3)T OB. Vf=(0 0…

A: Solution:

Q: 1. Find the following for the function f(x, y) = 3x³y² - 5x + 26y - 9.

A:

Q: Let f(x1, x2, X3)=( x1³ + x2, x1² + x3). Find df(1,2,3)(-3, –2, –1).

A:

Q: Determine and graph the domain set of the function f(x, y) = ln(x²+9y2-81) ==

A:

Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

A:

Q: dz 2 = -ry", where r = st“ and y = –st". Compute – as a function of s and t only evaluate this when…

A:

Q: a) If y = 3x – 2, x = 3t + 2, and t = 3k – 2, find b) Express y as a function of k ify = 2x + 5, x…

A: Introduction: A function is an expression, rule, or law in mathematics that defines a relationship…

Q: .Let f, g andh are three functions defined as below : f: R>Rf(x) = 4x² – 4, - g. R→R8 (x) = V-5x+…

A: Given  f(x) = 4x2-4g(x) = -5x+1h(x) = 2x-5   a) fog(x) = f(g(x)) = f(-5x+1) = 4-5x+12-4 =…

Q: Let X-(3, 4, 6, 8). Determine whether or not the relation R = {(x, f(x)) :x - X, f(x) %3D = x2 + 1}…

A: Solution is given as: Hope the answer is helpful.

Q: If f(x) is a linear function, f( – 5) = - 5, and f(5) = – 3, find an equation for f(x) Submit…

A:

Q: Find the autocorrelation function for the following functions. -1 2 -1

A: The mathematic expression of the first signal in its period is written as: x1t=tT   for 0<t<T…

Q: Let u and v be the linear functions defined asu(x)=2x+3,v(u)=3x-2.Find the compositions u*v and v*u.…

A: For uov, we do u(v(x)), and for v o u, we do v(u(x)) .

Q: Which of the following is not a function of x? Vx-4 a b x* +y = 4 C xy = 1 x² +y? = 1 d. %3D y = |x|…

A: Solution Y is a function of X if we can find it uniquely by x.

Q: Compute f, fy, f fy, and fr of the function. f(x, y)=(2x-3y)* |

A:

Q: Let T: P, → R? be the function defined by the formula T(p(x)) = (p(0), p(1)). Find T(5,4). Select…

A: We will assume a linear polynomial whose image is given to us. Now we will use the definition of T…

Q: Compute the following values for the given function. f(x, y) = 4x2 + 2xy – 7x + 4 f(1, 2) %3D f(2,…

A:

Q: Find real numbers a,b,c,d such that And then find f'(z) =? f(x) = x² + axy + by² +1(cz² + day + y²).

A:

Q: Q1 a) let f be a function defined as f(x)=3x² + 2x². Find f(2), f(-1), f(1). b) Define functions f…

A: