Let (t) = t³ – 4t² + t 10 8- and y(t) = t – 6t + 3 6- At t = 3, ¤(3) = -2- y(3) = da |t= dt dy t=3 = dt dy t=3 = tangent slope = da speed(3) = ||

Q: dy b) Find the equation of a curve if gradient of the curve at point (x, y) is given by- = 2x3 + x…

A: We have to solve the problem

Q: 1. Find the first differentiation of this equation: a. y = (Sx2-3)a b. y = (4x2 – 7)3 c. y Sx+6…

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Q: Find the derivative of the function

A: Given  that y = ( ax+ √(x2+y2)) -2 Method used- Chain rule- The chain rule states that the…

Q: An object is moving horizontally along a straight line. Its position, in metres, after t seconds is…

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Q: dy of the function: dx Find the derivative Зx3 — 4x2 + 5 + Vx- 2Vx5 y = | x2

A: The given function is  y=3x3-4x2+5+x3-2x5x2y=3x3-4x2+5+x13-2x52x2

Q: + 9y = sec 3x

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Q: 2) Find the equation of the curve whose slop 12 B) T= r The rate of change of the temperature, T (in…

A: Step 1: Step 2:

Q: 경기 Use implicit differentiation to find and 4x2 + 3y2 = 9 dx d²y 2 dx

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Q: Find y in terms of x. dy = x 2 + 5, curve passes through (0, 14) dx x3 A) y = + 5x 3 B y = x3 + 5x +…

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Q: Find y' if 3x2- (xy²) = 2y³ 2 3=

A: Given: 3x2-xy212=2y3   As we know that; The sum/difference rule: f±g'=f'±g' The Power law;…

Q: Derivatives Show that d(y,v)/dv = (1 – v?/c²)-2 for y, = 1/V1- v² /c².

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Q: 5 dy 3x4 – 4T + x2 Find the derivative dx, y

A: We have given the equation; We shall use the formula of derivatives that is;

Q: find dy/dx if y=((t-1)/(t+1))^2 and x= (1/t^2)-1 at t=2

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Q: Find the derivative of y = 3x² − 2x + dy = 6x 2 dx dy dx dy dx Oy = = 3x - 1 = 3x - 2 6x - 2

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

Q: The equation of the line tangent to the curve F (x) = S e dt at a = %3D V1- O y-V2 = (=- ) O %3D y -…

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Q: Use implicit differentiation to find y² + 4x³ = 8y - 5x² dy dz z(5+6x) y-4 da X

A: Topic = Derivative