Asked by habib
the derivative of 4xsin(x)cos(x)
Answers
Answered by
oobleck
using the product rule,
d/dx (4x)(sinx cosx)
= (4)(sinx cosx) + (4x) d/dx (sinx)(cosx)
= 4sinx cosx + 4x(cos^2x - sin^2x)
= 4(sinx cosx + x (cos^2x - sin^2x))
or, for less work,
4x sinx cosx = 2x sin2x
so the derivative is
2 sin2x + 4x cos2x
d/dx (4x)(sinx cosx)
= (4)(sinx cosx) + (4x) d/dx (sinx)(cosx)
= 4sinx cosx + 4x(cos^2x - sin^2x)
= 4(sinx cosx + x (cos^2x - sin^2x))
or, for less work,
4x sinx cosx = 2x sin2x
so the derivative is
2 sin2x + 4x cos2x
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