Sunday, February 28, 2016

Single Variable Calculus, Chapter 5, Review Exercises, Section Review Exercises, Problem 36

Determine the derivative of the function f(x)=sinx11t21+t4dt using the properties of integral.
ddxsinx11t21+t4dt=ddx(u11t21+t4dt)

g(x)=ddu(u11t21+t4dt)g(x)=ddu(u11t21+t4dt)dudxg(x)=1u21+u4dudxg(x)=1(sinx)21+(sinx)4cosxg(x)=(1sin2x)(cosx)1+sin4x (Apply Pythagorean Identity sin2θ+cos2θ=1)g(x)=(cos2x)(cosx)1+sin4xg(x)=cos3x1+sin4x

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