dy Given y = x" In (2x), determine dx a.x“-' In (2x) + а-1 None

Q: 3) Find dy dx a) y = x+In(sec 3x) %3D In(x+)

A: solution:-

Q: (a) (e* +In (y ))dx ++1 dy = +1 dy = 0 , y (In (2)) =1

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: dy Find dx x/3 S sin (P)at y = dy dx

A: Leibniz rule:

Q: dy In(3x + 7) Find for y = dæ 9e5z dy %3D dx

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Q: d y = -4 at x= 0. dx dy +2- +5y=0, where y = 2, dx dx

A: We have, the given differential equation as d2ydx2+2dydx+5y=0 Therefore, D2+2D+5y=0 Thus, auxiliary…

Q: dy In(4x + 4) Find for y %3D dx 5e4x dy %3D dx

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Q: dy at the given points. dx Find 5. x + 4xy + 2 y² + 3 = 0 .2 at (2,–1).

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Q: Let y=x2+2x. Compute Δy and dy at x=3 if dx=0.2. What is the difference between Δy and dy? That is,…

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Q: dy In(3x + 5) Find for y = - dx 8e3x dy %3D da

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Q: dy from the equation vx + y = 1 + x'y² dx Evaluate when x =1

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Q: ty = tan(4x + 2). %3D nd the differential dy when x 4 and dx 0.2 ind the differential dy when x 4…

A: Given, y= tan(4x+2)

Q: Find the differential dy, then evaluate: y= 2x3+ 6x-| when x= -2, dx= 0.l

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Q: dy| 2х — 6 - Find- , where y = dx\x=1 x + 2 Enter the exact answer. dy dx=1

A: Solve

Q: dy dx Find t3 de +1 ソニ 1-3x

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Q: 2. dz+a dy+y dx² Solue Sinx where e variation of parameter

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Q: dy given that In(x + y2)-tan- = 0. Find dx

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Q: Find dy/dx and d2y/dx2 without eliminating the parameter. x=1-t^(2), y=1+t

A: x=1-t2,  y=1+t Differentiating with respect to t, we get dxdt=0-2t  &  dydt=0+1⇒dxdt=-2t  &…

Q: Find dy/dx and d2y/dx2 of x= t + 1/t, y= t + 1

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Q: - 16y? – 16x – 16y = 0. dy at the point (3, dx ves to calculate

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Q: Q1-If x= cot- VE, y =, find d²y dx' dx2 at t = 2.

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Q: (b) Given that y(6x +1) e** = 1+ - In dy Find when x 0 and y=1. dx

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Q: dy y(ln y – In x + 1) dx

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Q: dx at x = dt dy Find - 5 if y = x² - 3 and = 4. dt

A: A detailed solution is given below

Q: dx at x = dt dy - 22 – 2 and dt – 5 if y = 4. Find - dx dt

A: We will find the derivative.

Q: Find of / dx and of /ay. f(x.y) = elx +y+6) of I dx = of I dy =

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Q: dy Find for dx 3) y = In(vx2 + 1+x) sin¯1x X.

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Q: Find dy/dx in terms of t if x = te', y = -5t – 5e dy/dx = [

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Q: y dx + x(Inx-Iny -1) dy z

A: Use substitution lnx=u:…

Q: find the dy/dx at x=-2 for y=3u^2 + 2u and u= (x^2+5)^1/2

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

Q: dy In(5a + 2) Find for y = %3D dx

A: Giveny=ln(5x+2)7e5xdifferentiate…

Q: dy for y=In (x² +1}+ (sin x +5)*. Find dx

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Q: dy Find of y* = sin(e) + xtan-'x %3D dx

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Q: dy 2) Find implicitly: dx (a) xy+3x2 =y? (b) exy – Iny =x? %3D

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Q: dy Given y= 5e3X + sin x, -is dx

A: differentiate y with respect to x  with the help of differentiation properties we will solve the…

Q: dy -y In (yecos)dx 4. COS Y sin x dx

A: The detailed solution is given below Thank you

Q: Find dy/dx at the given point without first solving for y. xy2 = 343 at (7, 7) dy %3D dx

A: Given query is to find the derivative of the expression.

Q: dy What is the value of dx at the point (1,0) if y = In(x² + y²)? %3D Undefined O 1 O 2

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Q: What is dy/dx at t = 1 when x = t^3 - t^2 and * Y = /3t – 1

A: Recall: If x=x(t) and y=y(t) then dydx=dydtdxdt d(ax+b)ndx =a.nax+bn-1

Q: Find the value(s) of dx at y=1 given that x²y+ y² = 5.

A: Given,        x2y+y2=5  and dydx at y=1

Q: Find the value(s) of at y= 1 given that x2y+y2 = 5. dx

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Q: (e* – sin y) dx + cos y dy = 0; when x = 0,y = 1 - %3D

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Q: Find the value(s) of dx at y= 1 given that x²y+y² = 5. only В only 2

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Q: dy Find the solution to dx 5xy which passes through the point (0, e). (In y)? y =

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Q: (y In y e") dx + +x In y dy = 0

A: The given differential  equation is of the form Mdx+Ndy=0. Identify the functions M(x,y) and N(x,y),…

Q: dy = y|* – sin x. In x when y equal to: dx

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Q: y.cos(z) dx dy dz * 0 0

A: Given that: ∫01∫0π∫0πy.coszdxdydz

Q: dy dx at x = dt Find 2 if y = – 5x² + 5 and = 1. - dt dx dt

A: Here we use the derivative formula. find dy/dx  there after we will use chain rule -. dy/dx =…