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How do you differentiate #g(x) = (1 + sin^2(2-x))(1 +cos^2(x)) # using the product rule?

1 Answer

Shwetank Mauria

Jun 19, 2016

#(dg)/(dx)=-sin(4-2x)(1+cos^2x)+sin2x(1+sin^2(2-x))#

Explanation:

Product rule states if #g(x)=f(x)xxh(x)#

then #(dg)/(dx)=(df)/(dx)xxh(x)+(dh)/(dx)xxf(x)#

Hence as #g(x)=(1+sin^2(2-x))(1+cos^2x)#

#(dg)/(dx)=(-2sin(2-x)cos(2-x))(1+cos^2x)+(1+sin^2(2-x))(-2cosx xx(-sinx))#

= #-sin(4-2x)(1+cos^2x)+(1+sin^2(2-x))(sin2x)#

= #-sin(4-2x)(1+cos^2x)+sin2x(1+sin^2(2-x))#

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