5. An object moving along a curve in the xy-plane has position (x(1),y(t)) at time dy dx t with di = cos(e') and = sin(e) for Os152. At time t = 1, the'object is at dt %3D www the point (3, 2). (a) Find the equation of the tangent line to the curve at the point where t= 1. (b) Find the speed of the object at t = i. (c) Find the total distance traveled by the object over the time interval 0si 2.

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A: Solve by derivation

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Q: 9) Find the equation of the tangent to the curve y = 1+ Int and x=t+Int when t = 2.

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A: Given: y=arctan(sinh(x)) Since, ddxtan-1fx = 11+fx2f'x Therefore, dydx=11+sinh2xcoshx

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Q: ind dy/dx by implicit differentiation for the curve  ex/y = x + y.

A: we differentiaite both sides with respect to x:

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A:

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Q: What is the first derivative of y=tanh(0³+30)? A y'=3(0²+1)sech (0²+30) dy =3(0²+ 1)sech²(0²+ 30) B…

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Q: find the total differential dz. xety

A: dz=∂z∂xdx+∂z∂ydy ---->1Consider z=xex+ythen∂z∂x=ex+y+xex+y∂z∂y=xex+y

Q: 3/20 What is the equation of the tangent line to the function y = e*- arcsin) at x= 0 ? A) y- -(1+)=…

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Q: derivative with

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Q: 4. Differentiate y with respect to x. y = (In Vcosh3x)(sinh(2x + 1) ex+1)

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