c = sec t, and y =

Q: If x sin(nx) = f(t) dt, where f is a continuous function, find f(64). %3D f(64) = %3D

A:

Q: Calculate D(fog) for the functions f(x, y, z) (st, tu, su).

A: answer is in next step

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: Let r, h, and A be differentiable functions of t and A = 2xr + 2rrh. Find dA/dt when r = 2, h = 5,…

A: Given, A=2πr2+2πrh

Q: If zis implicitly defined as a function of x and y by xy-yz+xz=0, find dz/dx. (y+z)/(y-x)…

A:

Q: At what point is the function in Exercise continuous?

A: Firstly, the expression can be thought as a combination of a linear function g(x)=x+2 and the other…

Q: Suppose that u and v are functions of x that are differentiable and that u (1) = 2,u′(1) = 0,v(1) =…

A:

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

A:

Q: Let f(z) = V sin(e=*cos(=)) f'(x) =0

A: We need to find derivative.

Q: Determine if the following are homogeneous or non-homogeneous functions f (x, y) = cos = cOS x + y f…

A:

Q: Let f(x) = x + vx . The equation for the tangent line at the point (1, 2) is y = m(x – 1) +2, where…

A: Given: fx=x+x

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 X and Y have a joint pdf f (x, y) = (2/3)(x + 1), for 0 < x < 1,0 < y < 1, zero…

A:

Q: Let f(x, y)= Jxy +x+xcos y. (a) Find fy - ở² f_ (b) Find дхду

A: f(x,y)=xy+x+x cos y

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A:

Q: If y is a twice differentiable function and x cos y + y cos x = t, find y"(0).

A: solve by differentiate

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Given:     x2 + y2 = 100

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Definition used-      Chain rule of derivative - For a composite function, we use the chain rule of…

Q: Find ∂z/∂x for1/x+1/y+1/z= 1. Assume that the equation implicitly defines z as a differentiable…

A:

Q: Find the tangent to y = cos x at x = 5- O A. y=x+7 O B. y= -x+7 O C. y= -x-7 O D. y= 1

A:

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

A: Given: f is a differential function of x and y . gu,v=feu+sinv,eu+cosv         Objective is to…

Q: Let g(x) be any differentiable function and let x – 1z = g(y – 11z) is given. For function z = z(x,…

A: This question is about application of derivative

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

A:

Q: Use convolutions to find an explicit function y(t) such that pt y(t) = 1+ | y(t) sin(t – æ) dæ.

A:

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

A:

Q: Find the linear approximation to f(x)= cot (x) LCx) = f (a) + f'Ca) (x-a). near a=" as

A:

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

A:

Q: Let r and y be differentiable functions of t and suppose that they are related by the equation ry –1…

A:

Q: 11.2.4. f(x, y) = V]xy|.

A:

Q: Let Y and Y have the joint pdf f (x,y) = 6(1– x – y), x+ y < 1, 0 < x, 0 < y, zero elsewhere.

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Let x and y be two differentiable functions of t. Given y = 1/ x , find d y /d t if x = 5 and d x d…

A:

Q: The function f(z)=e^(-y) sin⁡x is analytic function

A: Here, f(x,y)=e-ysin x          =e-ysin x+i(0) So, let u=e-ysin x, v=0 Now, ux=e-ycos x and vy=0 So,…

Q: y = a"

A:

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A:

Q: f (x) = sec? x +1

A:

Q: define y as a differentiable function of x,  find the value of dy/dx at the given point. 25. x3 -…

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: Let X and Y have the joint pdf f(x, y) = (1 – xy), 0 < x < 1, 0 < y < 1. Find E(X).

A: The given joint pdf is fx,y=431-xy,0&lt;x&lt;1,0&lt;y&lt;1.

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: Let f (x, y) = csc(x + y³) ey , find дудх

A: The given function is  f(x,y)=csc(x+y3)exy. The main objective is to evaluate ∂2f∂y∂x.

Q: Let u be a differentiable function of x. For the following functions , find dy/dx

A:

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: Assume that x and y are differentiable functions of t. For the following, find  dx/dt given that x =…

A: Differentiate both sides with respect to t

Q: Consider the function f defined by f(x,t) cos(r) exp(t)

A:

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: Let X and Y have the joint pdf f(x, y) = (1 –- xy), 0 < x < 1, 0 < y < 1. Find V(X).

A: let X and Y have the joint pdf f(x,y)=43(1-xy),   0&lt;x&lt;1, 0&lt;y&lt;1 marginal density function…

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: (a) Differentiate the functions w.r.t t, ddtx2+y2=100 2xdxdt+2ydydt=0 Substitute the given values,

Q: y = cosh u

A: Consider the given: y=coshuApply Chain Rule:dydx=dydu⋅dudx

Q: Given y=h(x).p(x),where h(x) and p(x) are differentiable function of x,show that dy/dx…

A:

Q: Let f (x, y) = x+ y Evaluate . f (x,y)ds when x sin t, y = sin t

A: Explanation of the solution is given below...