Question

if Y=sin^4 x + cos^4 x , find dy/dx
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Answer 1

given,

y=(sinx)^4+( cosx)^4

differentiate with respect to x

then

(dy/dx)=[ 4(sinx)^(4-1) ][cosx]+[4(cosx)^(4-1)][-sinx]

(dy/dx)=4(sinx)^3(cosx)-4(cosx)3(sinx)

(dy/dx)=4(sinx)(cosx)[ (sinx)^2-(cosx)^2 ]

(dy/dx)=-4(sinx)( cosx)[ (cosx)^2-(sinx)^2 ]

(dy/dx)=-4(sinx)(cosx)(cos2x)