(a)Find the equation of the tangent line to the curve 8x'y - 5x? + 7y° = 10(x-3y), at the point (2,-2). e*; -3x. (b) Given that f(x,y) = 6x³y³ - cosx + 5y-siny + 10x²- find f; fw i fy; f %3D ух

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A:

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Q: 3x2 + 5y2 = 8 curve is given. a) Find an equation for the tangent line at (1,-1) 24 b) Show that y"…

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Q: Q3) find the derivative of each function: 1) y=x sin 2x +x cosx

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Q: find (y" ) for the following equation 3x²-2y'-y=6 at point (2,1)

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Q: Consi ider the ellipse 4x² + 2xy + 5y² The derivative = d on this curve is

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Q: 2xy - y² + x = 2 at the point (1,2). - Find the equation of the tangent line to ² +2

A: By using equation of tangent line formula, we find the required tangent line.

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.