An observer moves so that his position, velocity, and acceleration at time t are given by the formulas r(t) = x(1)i+ y(1)j+¿(1) k, v(1) = dr/dt, and a(t) = dv/dt. If the temperature in the vicinity of the observer depends only on position, T = T(x, y, z), express the second time derivative of temperature as measured by the observer in terms of D, and Da. %3D %3D

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 1. Z= ;d'z/dx² 1+x2 2. Y (3x+2)* ;y" 3.…

A: 1) Given: Z=21+x2 Differentiating Z with respect to x, dZdx=2×ddx1+x2-1       =2×-11+x2-2×ddx1+x2…

Q: Compute the indicated derivative using the chain rule. dy x = 4 + 3t, y = -7t; dx dy dx ||

A:

Q: Compute the indicated derivative using the chain rule. x = 6 + 3t, y = −8t;  dy dx

A:

Q: Compute the indicated derivative using the chain rule. dy x = 1 – t/3, y = 8t – 1; dy %3D

A:

Q: dx y=u(1+u°)³ and u =(3x-2)². %3D Express the derivative in terms of x, if

A:

Q: 4. Use the chain rule to find out the total derivative dv/dt, when v = xe/z, where r = t²,y = cos t,…

A:

Q: What is the derivative of y = 34? a. y (4)(3**) b. y = 4x3 c. y = (4)(3*) In(3) d. y' = In(4x) + 34*…

A: We can answer all three subparts as below.

Q: z = Vx4 + yf, fz (1, 2)

A:

Q: Compute the indicated derivative using the chain rule. dy x = 5 + 3t, y = -8t; dx dy %3D dx

A: We have to find the indicated derivative by using chain rule: x=5+3t, y=-8t Differentiating first…

Q: he derivative of f(x,y)=10x^y at (e,1) in the direction of v = is

A: From the expression of the directional derivative:   D.D=∇fpx,y,z·a→a→   Given:…

Q: Find the derivative of y with respect to 1. y = In V4x2 + 7x %3D 2. y = sec?(e-4*)

A: A detailed solution is given below.

Q: Calculate the derivative of y with respect to x, if x/2 +y 3/2 = 7. dy dx

A:

Q: Find the third derivative of ƒ (z) = VT2z+I. f" (z) =

A: We use the exponent rule and chain rule.

Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1,1) in the direction of from the…

A: We have to find the directional derivative.

Q: What is the derivative of (6 x+1)5 (4 x-21)16 (21 x-23)3 (3 x+25)4 y = In with respect to x?…

A:

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 1. y= ;d'y/dx 2. Y = (7x + 2)S ;y"…

A:

Q: Compute the indicated derivative using the chain rule. X = 4 + 3t, y = -7t; Oy

A:

Q: Get the first order derivative of the function x + sin(y – 2x) - 1= 0 - 2 1 a. y' = cos(y-2x) 1 b.…

A:

Q: If we are getting the partial derivative of f(x,y) with respect to x, we are letting the y variable…

A: hello greetings from bartelby.i am here to help you.

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

A:

Q: y=In(x dy -

A: Given : y = ln1xx-5

Q: y" +6y' +10y=0; y(0) = 2, y'(0) =

A:

Q: Find the derivative of y with respect to the appropriate variable. y= cosh 2x+2 O A. V(4x + 9)(x +…

A:

Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

Q: _6. What is the derivative of f(x) = (5 – x²)²? а. 2(5- х2) b. 10 – 2x2 C. 4x3 – 20x d.(5 - x?)(5 -…

A:

Q: 23.3 Use centered difference approximations to estimate the first and second derivatives of y = e*…

A: The formula for the first derivative of a function fx at x=a by centered difference approximation is…

Q: What is the derivative of y = sin1 (x² + 2)? dy dr /1-(z²+2)² dy O dr 2x V1-(2²+2)² O dz V1+(x²+2)²…

A:

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: What is the first derivative of y=tanh(0³+30)? A y'=3(0²+1)sech (0²+30) dy =3(0²+ 1)sech²(0²+ 30) B…

A:

Q: What is the derivative of y = tan-1(x2 + 1)? dy dr 2 1+( z²+1)² dy dr /1+(z²+1)² dy O dr V1+(2+1 )°…

A: To find derivative of y=tan-1x2+1

Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8

Q: If z = (x + y) e and x = 6t and y = 1 – t, find the following derivative using the chain rule. Enter…

A: In this question we have to find the differentiation of z with respect to t.

Q: Find the first-order partial derivative with respect to x of f(x,y) = e5x siny.

A: To find the first-order partial derivative with respect to x, given function, fx,y=e5x sin y

Q: What is the approximate value of the first derivative of S(x)=-0.1x*-0. 15x-0.5x-0.25x-1. 2 at…

A:

Q: If z = (x + y) ev and x = 5t and y = 1 – t², find the following derivative using the chain rule.…

A: We are given that z=(x+y)ey,  x=5t, and y=1-t2. Now, we need to find dzdt.

Q: The population of a city is associated by the function P(x,y,z)=x² + 2y² + 2z². If the population of…

A:

Q: 2. Find the critical points of f(x, y) = x³ + 2y³ – xy and analyze them using the Second Derivative…

A:

Q: If z = xy and x = e=' and y = sin(t), find the following derivative using the chain rule. Enter your…

A:

Q: y" – 4y' +4y = 0; y(0) =-1, y'(0) = 0

A: We have to solve the differential equation…

Q: If z = (x + y) e and x = 3t and y = 1 – t, find the following derivative using the chain rule. Enter…

A:

Q: dw B) Use the chain rule to find the derivative dt of w = x2 + y2 with x cost, y = sint.

A:

Q: B: Use the Chain Rule to find the derivative of f(x,y) = xy with respect to (t) along the path y =…

A:

Q: Find the derivative of g(x) = |. •r In z Vt2 +t+1 dt

A:

Q: Find the derivative of the function. y = (3t – 1)(6t – 6) -1 dy dt II

A:

Q: Find the 1st and 2nd derivative of: Vx + Jy = va

A:

Q: 1. F(x) = S, t³ - 5t dt

A:

Q: Find the gradient of the tangent to the curve xy“ + y+ ( log_(x – 2))² = 14 at the point (3, 2).

A:

Q: Find the maximum directional derivative of the function f(x.y) = x In y + x2y2 at the point (-1,1).…

A:

Q: Find the derivative of f(x, y) = e- x ln(y² + 1) at the point R(4,0) in the direction of w = (2, 1).

A: NOTE: Refresh your page if you can't see any equations. . the given vector is find the unit vector