If the rate of change of x is 2 unit #s^-1#, Find the rate of change of y in #y=3/((2x-3)^3# when x=2?

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Answer 1 · 2018-01-31T17:22:50

# "The reqd. rate="-36" u/sec."#.

#y=3/(2x-3)^3=3(2x-3)^-3#.

Diff.ing w.r.t. #t# using the Chain Rule, we have,

#dy/dt=d/dx{3(2x-3)^-3}*dx/dt#,

#={3(-3)(2x-3)^-4*d/dx(2x-3)}*dx/dt#,

#rArr dy/dt=-18(2x-3)^-4*dx/dt#.

Here, #dx/dt"=the rate of change of "x=2" u/sec."#,

The reqd. rate of change of #y=dy/dt#.

#:."The reqd. rate="[dy/dt]_(x=2)#,

#=[-18(2x-3)^-4]_(x=2)*(2)#,

#=-36{2(2)-3}^-4#.

#rArr "The reqd. rate="-36" u/sec."#.