1.Assume that x and y are functions of t. If y=x^3 +2x and dx/dt =4, find dy/dt
ID: 2883912 • Letter: 1
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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