What is the derivative of $f(x) = xcos(x^2)+x^2sin(x)$ ?

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Answer 1 · 2018-03-23T12:24:11

It is given that, $f(x)=xcos(x^2)+x^2sin(x)$

Applying product rule to each term,

$f'(x)=[x'*cos(x^2) + x*cos(x^2)']+[x^2'*sin(x)+x^2*sin(x)']$

$=>[cos(x^2) + x*-sin(x^2)*2x]+[2x*sin(x)+x^2*cos(x)]$

$=>cos(x^2) -2x^2sin(x^2)+2xsin(x)+x^2cos(x)$

What is the derivative of f(x) = xcos(x^2)+x^2sin(x)f(x) = xcos(x^2)+x^2sin(x)?