1. Find dy/dx given tan(xy)=7x+2y. a) dy/dx=(7ysec(xy)tan(xy))/(xsec(xy)tan(xy)2

Question

1. Find dy/dx given tan(xy)=7x+2y.

a) dy/dx=(7ysec(xy)tan(xy))/(xsec(xy)tan(xy)2)

b) dy/dx=(7ysec^2(xy))/(xsec^2(xy)+2)

c) dy/dx=(7ysec^2(xy))/(xsec(xy)tan(xy)2)

d) dy/dx=(7ysec^2(xy))/(xsec^2(xy)2)

e) dy/dx=(7+ysec^2(xy))/(xsec^2(xy)2y)

2.

A heap of rubbish in the shape of a cube is being compacted into a smaller cube. Given that the volume decreases at a rate of 3 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 8 cubic meters.

a) 3/4

b) 3

c) 12

d) 4

e) 1/4

Explanation / Answer

1. Find dy/dx given tan(xy)=7x+2y

differentiate on both sides

sec2(xy) *(y +xdy/dx)=(7*1 +2dy/dx)

ysec2(xy) +xsec2(xy)dy/dx=7 +2dy/dx

(xsec2(xy)-2)dy/dx =7-ysec2(xy)

dy/dx =[7-ysec2(xy)]/(xsec2(xy)-2)

2)volume v =x^3

v=8 ==>x^3 =8 ==>x=2

dv/dt =3x^2 dx/dt

given dv/dt =-3cubic meters per minute

-3=3*2^2 dx/dt

dx/dt=-1/4

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