at the position of a particle is between x and x + dx is f(x) dx where 2πχ (Nsin² (2) when 0

Q: Find the equation of the normal at (1,2) for the function 2x - 3xy+ y +x+2y+12%3D0.

A: Equation of normal for a  curve at a point (a,b) is given by, y-b = m(x-a) Where m is the slope of…

Q: Find the derivative, dy/dx: y = x² In x3 ý =- 2 1-4 ln x x³ In? x 3. ý = -2 In x – 2x | y = --(- 3…

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Q: Find the implicit deriviate (dy/dx) of (2x+3y)1/3=x2

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Q: find dy/dx if y=xcosx+x2sinx

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Q: Show that the slope dy/dx is defined at every point on the graph of 2y = x² + sin y.

A: Given- 2y=x2+sinx To prove- That the slope dydx is defined at every point on the graph of the above…

Q: Find the derivative dy dx dx of the function y = sec (1 + 4 + sin ¹(4 + ²)

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Q: Calculate the derivative indicated in the figure below

A: rs=s, 2s, s2

Q: Find the derivative of y with respect to s. y= sec 1(7s° + 4)

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Q: Let f(x) = 3x+ 4x. Evaluate dy when x=2 and dx=0.1

A: Given that fx=3x2+4x To evaluate dy when x = 2 and dx = 0.1.

Q: Find the gradient function (dy/dx) of y=e-2x tanx. Show all calculations.

A:

Q: . Find P.S. of (16x +5y) dx + (3x+y) dy = 0 of the curre to pass thru the point (1,-3) 2. Find P.S.…

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Q: Find dy/dx at the point (2,1) if 4y3-x2y2=0

A: Given that: 4y3-x2y2=0

Q: X.

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Q: Calculate the derivative.

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Q: y = x³ + 4x - 15 at x = 0

A: Formulas to be used: 1) Newton's Forward Difference Formula The formula for the forward difference…

Q: 2. Differentiate. f(t) = et sin(2t)

A:

Q: Let 3x3-y3 = 2. What is the value of dx/dt if dy/dt = -2 when x = 1?

A: To find the derivative of x with respect to t.

Q: Find the derivative. 1 y = _x3 + 3x + Væ 2 Ody dx O Ody dx || ip O 32 y=2x2 +3 + 2x 32 || 2 X +3+1/x…

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Q: dy Part II: Find the derivative ) implicitly. Show all work. dx 11. e" – 4x³ + 5y? = 10

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Q: ) Find y as a function of x if x?y" + 2xy' – 42y = 0, y(1) = 5, y'(1) =-3. y =

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Q: d sec(11x – 4) dx = dt 13

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Q: #4 y=sin(0.5√√x)/x at x = 1

A: dfdx=fx-fx-hhd2fdx2=fx-2fx-h+fx-2hh2 y=fx=sin0.5xxx=1h=0.25∴dfdx=fx-fx-hh          =f1-f1-0.250.25…

Q: Find the equation of a curve if d²y 4 = dx² (2x - 1)² the curve passes through (5, 2 ln3), and the…

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Q: 1. Find dx dy for the following functions: 1) y = (x- 3)(1- x) (ans.:4 - 2x) b (ans. :-,) x* 2) y=…

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Q: Find dw/dr and dw/dΘ for w=2z/y-3x if x=3Θ+2r, y=3r^2 + Θ, and z =4r-Θ, where Θ = 2 and r = 5.

A: w=2zy-3xx=3θ+2r,y=3r2+θ, z =4r-θTo find ∂w∂r and ∂w∂θ for θ=2 and r=5

Q: Find y". 6. 7. y =x' +6x y'"3= %3D

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Q: 4 y = x + + Vx

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Q: dy 1 is dx 2Jx Example 3: Show that the derivative of y= Vx

A: See the attachment