H.W: Determine which the following functions are differentiable. a) f(z) ix ze.e 6) f(Z) =

Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), e" + cos(v)). Use…

A: Using total derivatives:

Q: Suppose that y and z are twice-differentiable functions of r. Show the d y dr y z %3D y"

A:

Q: For what vaļue of x does the function g(x) =x - 2x? strictly convex? В. x> 0 A. x> 2 D. x -2

A: From the given problem:   gx=13x3-2x2   As we know that:   If f''(x)<0. then function strictly…

Q: f(z) is a twice differentiable function with f(0) = 1, f(2) = 4, f'(2) = 5, Then af"(x)dx = %3D

A:

Q: n (p hix ( %3D what is the dependent vaniable in

A: Solution

Q: a² + y? – a*y³ f(r, y) x² + y?

A:

Q: Find the point where the CAUCHY-RIEMANN equation is satisfied for the function? f(z) = xy2 + x²yi

A:

Q: Let f be a differentiable function of one variable, and let f(p), where p = (x² + y² + z²)'/2. Show…

A:

Q: The domain of the function y tanh z is 1, +∞). Select one: a. False Ob. True

A: To find the domain of this function, we use the fact that for any one-to-one invertible function f…

Q: Let y = f(x) be a derivable function implicitly defined by the equation x2 + y2 = 1 . Calculate y'.

A: The power rule of differentiation to differentiate a function of the form y=xn,is stated as…

Q: Suppose that the radius r and surface area S = 4pai r2 of a sphere are differentiable functions of…

A: The relation between surface area and the radius of the sphere is as below.

Q: H.W Is f (x) = x. |x| differentiable function? %3D

A: To find  f(x)=x|x| is differentiable function or not.

Q: Answer the following True or False: 3 and f(7), S() Is horizontal at z C. 3. Then there exists a c…

A: According to Rolle's theorem- If a function f(x) is differentiable from x=a to x=b. And the values…

Q: The volume of a right-circular cone of radius r and height h isV = π/3 r2h. Suppose that r = h = 12…

A: Consider the given: Volume,V=π3r2hr=h=12 cmDifferentiate w.r.t. "r",dV=π32rdrh    ⋯⋯11cm increase in…

Q: Suppose that the radius r and volume V = Tr³ of a sphere are differentiable functions of t. Write an…

A:

Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)\/2,…

A: In the given question we have to prove the equation.

Q: stead of f(x)). E

A: answer is in next step

Q: 21 Find the value of c such that the line y = -x + is tangent to the curve y = c/x.

A: Given line ⇒y = 76x+212    .....(1)curve y = cx   ....(2)Differentiating w.r.t 'x'       (2)y' = c2x…

Q: faow that the function f depthed by (X .Y) = (1, - 1) f(XrY) = %3D x2 + 냉 (x, y) $ (1,-1) * ty is…

A:

Q: Given the equation y In (x? + y² + 4) = 4, evaluate dy Assume that the equation implicitly defines y…

A:

Q: c = sec t, and y =

A:

Q: If the equation x²e+z_224cos(x-224z)=n?e+224 defines z implicitly as a differentiable function of x…

A: Since you have asked multiple questions, we will solve the first question for you. The other…

Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)!/2.…

A:

Q: Fx = - to find dy Assuming - 3x - 2y? + xy = 0 defines y as a differentiable function of x, use the…

A: Y as a differentiable function of x and find dy/dx at the point (-1,1)

Q: Calculate the derivative of the following functions

A: Given: y=fx gx5 To determine: Derivative of the given function

Q: On what interval is the following curve concave downward? (Enter your answer using interval…

A:

Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)\/2.…

A:

Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), e“ + cos(v)). Use…

A:

Q: a2z Find given that z is a differentiable function of x and y, and xz + yz3 = 2 + x?ev

A:

Q: Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e"F…

A: Given that zx,y=eyFexy where F(t) is differentiable function . Prove that xzx+yzy=yz

Q: 4. Determine the set of points at which the function is continuous. cos(xy) b) f(x,y) = e? – y? '

A: we have to determine the set of points at which the function is continuousgiven function,…

Q: Verify that the conclusion of Clairaut's Theorem holds for the function: f (x, y) = e*y sin(y)

A:

Q: If C is any piecewise-smooth simple closed curve in R? and f and g are differentiable functions,…

A: Solve the following

Q: at the point (0, 3, Given that the relation y + yz = 14 - sin(xz) + implicitly defines x as a…

A:

Q: Suppose f is a differentiable function of x and y,and g(u,v)=f(eu + sin v, eu + cos v). Use the…

A: Given that f is a differentiable function of x and y and g(u, v)=f(eu+sin v, eu+cos v).It is…

Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), eu + cos(v)). Use…

A: To solve the given problem

Q: Determine the domain of the function f(x, y) = In(r? + 2y? + 1) + arccos 1-r

A: The domain of a function is the set of values of the variable for which the function gives a defined…

Q: ax +b. N<2 Given fx) - find a & b such that f is differentiable at 2. 1212-1, x22

A:

Q: Let f: R2 → R. At some point, a , we have that f(a) = 5 and that Vf(a) : What is the equation of the…

A: answer is in next step

Q: Suppose r lIs a differentiable function of x and y, and g(u, V) = (e sin(V), V)). Use the table of…

A:

Q: 6. If y is a differentiable function of r and 24 + 2y5³ 5y2, then find - dy da

A: The given equation is x4+2y5x3=5y2

Q: A model created by an engineer is represented by the following multivariable functions x = t'u, w =…

A: As per Bartleby guidelines we're supported to answer only first three subparts. Kindly repost rest.

Q: Find the domain of the following multivariable functions (answer two) f(x,y) = /4 – x² – y b.…

A: (a) Given that           f(x,y) = 4-x2-y2   Domain:       Since                      4-x2-y2⩾0 ⇒…

Q: , Consider the function f(x, y) = x'y + y – 27y. f has v at (3/3, 0). f has ? at (0,0). f has ? v at…

A:

Q: A. Consider the following multivariable function z : = z(x,y) where a CX y-b where {a,b,c} are…

A: follow next step

Q: 4. Suppose that c is a constant and that u is a continuous, differentiable function of x. Show:…

A: prove of the above question is given below...

Q: Suppose that f:I → R and g: I → R are differentiable at c E I. Then, a) If k E R, then the function…

A: