How do you use the chain rule to differentiate #y=(2x-7)^3#?

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Answer 1 · 2017-08-09T11:39:07

#6(2x - 7)^2#

#rArr y = (2x - 7)^3#

Let #(2x - 7) = t#
#therefore x = (t + 7)/2#

then, #y = t^3#

So, #dy/dt =3t^2#

Also, #dx/dt = 1/2#

Now, #dy/dx = dy/dt * dt/dx#
#therefore dy/dx = 3t^2 * 2 = 6t^2#

Hence, #6t^2 = 6(2x - 7)^2#

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