In r Consider the function F(x)= dt (for r>0). What is F'(x)? %3D F'(x) = e In a O F'(2): In r In x F'(x) - 1 F'(교) = In r

Q: Determine the instantaneous rate of change of the function πt ³ √x sin 2 f(x) = LV x3 1 + √t at x=2.…

A: Leibnitz integral rule.

Q: 1. Suppose y = f(x) and that x is changing over time. How is dy/dt related to dx/dt?

A: Given that: y=f(x)

Q: A particle is traveling upward and to the right along the curve y = ln x. Its x-coordinate is…

A: Given:

Q: We are given the function f(x,y)=sin(3x+2πy)+exy-π, and points A(π, 1), B(π + 1, 0). Find the rate…

A: Given function is, fx,y=sin3x+2πy+exy-π. To find the rate of change of f at A(π,1) along the…

Q: dx dy Find at x = 1 if y = – 5x´ – 3 and 5. - dt dt dx dt

A:

Q: Find partial derivative af dx for the function f(x,y) given below exp 2x. siny .(at the point (In2,…

A:

Q: x tan(yz) ey – 4x3z2 3: Find the total derivative of f(x, y, z) =

A:

Q: Inx dx, 2. Integrate (1) using the substitution u = In x (ii) using integration by parts.

A: Integration by substitutions and by parts

Q: Find the differential of the function f(x,y)=x(e^-y) at (2,0). df=?

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: Find the total differential. z = 10x"y3 dz =

A:

Q: Find the total differential dz ZzxeX+y

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Given that x and y are functions of time, find the indicated rate of change. dx when x 6, y = 3, and…

A:

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

A: The given function is  y = 2x2 + 1; dx/dt = 2 centimeters per second

Q: Find maximum rate of change of f at the given point. f(x,y)=sin(xy), (1,0)

A:

Q: if z=tan-1 (y/z) where x=lnt and y=et . Find (dz/dt)

A: Given,          z=tan-1yz where x=lnt and y=et

Q: dy at x = 1 if y = 4x² + 1 and dt dx Find – 1. dt dy dt || ||

A: Solve the following derivative

Q: If f(x, y) = y cos(x) – x* In(y), find the second partial derivative (A dx? -y? cos(x) – 6x In(y) d…

A:

Q: Find the total differential of the function. 5x + у f(x, у, 2) y + 3z df =

A: Total differentiation

Q: 6. Suppose that w = x cos(yz²), where x = sin t, y = t² and z = 2e'. Find the rate of change of w…

A: Using derivative

Q: The maximum rate of change of the function f(x,y,z) = x In(yz) at (1;2;) is equal to: V17/2 None of…

A:

Q: Find the total differential w = x2yz2 + sin yz

A: Partially differentiate w = x2yz2 + sin yz with respect to x and keep y and z as constants.…

Q: Find the total derivative of the function f(x, y, z) =+z In (2x+1)+sin (xy) xz

A:

Q: d²x dx + sinx=0 +2. dt for small excursion about x = T/4. 1. Linearize dt

A: d2xdt2+2dxdt+sin x = 0 - (i)here, the above given equation is homogeneous (RHS=0) but non-lineardue…

Q: # 5) If y = x³ + 2x and dx/dt = 5, find dy/dt when x = 2. # 9) If a snowball melts so that its…

A:

Q: Let xy = 3 and dy/dt = 4. Find dx/dt when x=2?

A: Given :                xy = 3  , dydt = 4 To find :                      dxdt when x=2

Q: 4. Given xy+x*y=2 such that d/dt =2 in/sec. Find dy/dt for x= 1

A:

Q: Compute the differential dz of the function. z = x*y" ,7,,11 dz

A:

Q: A particle moves along the curve y = x3/2in the first quadrant in such a way that its distance from…

A: Let w de the distance between origin and the particle at any time t. Given that, dwdt=11 Now by…

Q: dy Find at x = dt dx - 1 if y = 2x? – 3 and dt - 2. dy dt ||

A: y = 2x2 - 3dxdt = -2dydt = ?   at x=-1

Q: Determine the instantaneous rate of change of the function f(x) = [x² si sin (2¹) 1+√t x3 At x=1 dt

A:

Q: Find the general and particular soulution of dy/dx=3y, where y=6 and x=0

A:

Q: 7. By differentiation (and having a suitable choice of integrating constants) show that L. f(s) ds+…

A:

Q: Find the total differential of  w=x3yz+xy+z+3

A:

Q: (tiy t 3y" -x)dn + x (x+ Jdy = 0 2

A: Given differential equation is  4xy+3y2-xdx+xx+2ydy=0 find the general solution of the given DE

Q: find the general selution of the differential equetion by the fimear methodi sxy'-2y=x

A:

Q: The time rate of change of liquid circulating in two tanks is govemed by dy -0.02x + 0.02y, = 0.02x…

A:

Q: Find the total differential dw. 5. w = x tan¬ y – 2ªyz

A: The objective is to find total derivative dw.

Q: at is the maximum rate of change of f (x, y,z) at P?

A:

Q: Find the total differential. z = 10x6y7 dz =

A: Differentiation of xⁿ = nxn-1

Q: dy = 3; find dt dx when x = 2. dt Related Rates: Given y = x³ – 2x and

A:

Q: Let y=sqrtX. Find dy/dt when x=4 and dx/dt=3

A: →Use chain rule of differentiation.→dxndx = n xn-1     When n = 12         dx12dx = 12 x12-1…

Q: Suppose both x and y are functions of time (t). Find the rate of change of y with respect to t, that…

A:

Q: Find differential of the function y=(x^2+3)^3 dy=? dx When x=4 and dx=0.05, compute the…

A: We have to find

Q: Find the integrating factor μ(x) of y' + 4y - tan(x) = 0 such that μ(0) = 1. μ(x) =

A: See the details solution in below

Q: dx o ex+x е. f. S sin(vE) dt S dx 2x cos(vE) dt COS g. dx 'x

A:

Q: Find dy/dx by implicit differentiation. VTy = x'y +33 dy/dx =

A: The given equation is xy=x7y+33.

Q: What is the integrating factor of 2ydx + x (x² ln y – 1) dy = 0 ? Oy O y?

A: Question is solved.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.