1.Assume that x and y are functions of t. If y=x^3 +2x and dx/dt =4, find dy/dt

Question

1.Assume that x and y are functions of t. If y=x^3 +2x and dx/dt =4, find dy/dt when x=1. dy/dt=
2. Suppose x,y, and z are positive functions of t. If z^2=x^2+y^2, dx/dt=1,and dy/dt=2,find dz/dt when x=8 and y=15. dz/dt=
1.Assume that x and y are functions of t. If y=x^3 +2x and dx/dt =4, find dy/dt when x=1. dy/dt=
2. Suppose x,y, and z are positive functions of t. If z^2=x^2+y^2, dx/dt=1,and dy/dt=2,find dz/dt when x=8 and y=15. dz/dt=
dy/dt=
2. Suppose x,y, and z are positive functions of t. If z^2=x^2+y^2, dx/dt=1,and dy/dt=2,find dz/dt when x=8 and y=15. dz/dt=

Explanation / Answer

From the given question,

1. y=x3 + 2x

differentiating both sides with respect to t,

dy/dt= 3x2 dx/dt + 2 dx/dt

given that dx/dt =4. x=1

replacing it in dy/dt= 3x2 dx/dt + 2 dx/dt

dy/dt= 3x12 x 4 + 2 x 4

dy/dt =20

2. z2 = x2+ y2

differentiating both sides with respect to t,

2z dz/dt = 2x dx/dt + 2y dy/dt

given that dx/dt =1, dy/dt=2, x=8, y=15

replacing in z2 = x2+ y2

z2 =82 + 152

=64 +225=289

z=17

repalcing it in 2z dz/dt = 2x dx/dt + 2y dy/dt

2 x 17 x dz/dt = 2 x 8 x 1 + 2 x 15 x 2

34 dz/dt = 16 + 60

dz/dt= 76/34

dz/dt= 38/17

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