How do we differentiate #f(x)=sin^4(4x^2-6x+1)# using chain rule?

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Answer 1 · 2017-04-19T16:41:37

Please see below.

For #y=f(x)=sin^4(4x^2-6x+1)#, we can follow the order,

#f(x)=g(x)^4#, #g(x)=sin(h(x))# and #h(x)=4x^2-6x+1#

Hence #(dy)/(dx)=(df)/(dx)#

= #(df)/(dg)×(dg)/(dh)×(dh)/(dx)#

= #4(g(x)^3)×cos(h(x))×(8x-6)#

= #4sin^3(4x^2-6x+1)cos(4x^2-6x+1)(8x-6)#

= #8(4x-3)sin^3(4x^2-6x+1)cos(4x^2-6x+1)#