83. Second Derivative for a Parametrized Curve Given a parametrized curve c(t) = (x(t), y(t)), show that x'(t)y" (t) – y'(t)x"(1) x'(t)? d (dy dt dx Use this to prove the formula x'(t) y"(t)- y'(t)x" (t) d²y dx2 13 x'(t)3

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A: Topic = Derivative

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Q: 1) Find dy/dx by implicit differentiation.   sin(x) + cos(y) = 7x − 4y

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Q: Explain of the method of proving the derivative (dy/dx) of y=U(x)ᵛ⁽ˣ⁾ where U(x) and V(x) are…

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A: We can find the tangent line as below

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Q: 2. Find the equation of the tangent plane to f(x,y) = sin(x² +y) when x = 0, y = T. 3 and r - cost

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Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction of 4i -3j b)…

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Q: Find the derivative dydx of the parametrically defined function x=t+2sinπt, y=3t−cosπt at t=12

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Q: (5) Find the derivative dy/dx, where: 4 1 -1 y=- y = cosec(cot3x), y=Vsinh¯3x 3 1+ cos° x

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Q: 5. Use Implicit differentiation to find dy when y V x2 tya = 15x° +4siny 3

A: Using implicit differentiation find dydx for;  yx2+y2=15x3+4siny

Q: 4. Get the exact a. dy = cos 2x dz differentials of y = (sin 2)² b. dy=sin 2z dz dy = sin 2x d.…

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Q: Find the equation of the normal line to the curve f (x) = 6e2x cos x at the point (0,6). %3D

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Q: Find the solutton of followins ordinery differential e quation. yl- 2y' +y

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Q: 8. Find ihe point where the normal to y = x + Vx at (4,6) crosses the y-axis.

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A: Solution:-

Q: ey sin x = x + xY %3D

A: Solution:- The given implicit function is  ey sinx=x+xy

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Q: derivative of y with respect to x. y= In (6 In x) dy dx %3D

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Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)V(x) where U(x)and V(x) are…

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Q: Find the length of the curve y= ln sec x, Oln OIn 2+y3 V3 OIn 2+/3 OIn V3 2-V3

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Q: 2. Prove the formula of the derivative of y = cosec-f(x). d²y and dx2 of the parametric equation…

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Q: 1 dy if y = dx -1 Find - tan 3x. dy dax

A: Use derivative formula