How do you determine the derivative of $x cos x$ $xcosx$ ?

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How do you determine the derivative of $x cos x$ $xcosx$ ?

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Answer 1 · 2016-12-17T14:31:38

Find the first derivative and then differentiate again.

$\frac{d y}{d x} = 1 (cos x) + x (- sin x)$ $dy/dx= 1(cosx) + x(-sinx)$

$\frac{d y}{d x} = cos x - x sin x$ $dy/dx = cosx - xsinx$

Differentiate again.

$\frac{d^{2} y}{{d x}^{2}} = - sin x - (1 (sin x) + x (cos x))$ $(d^2y)/(dx^2) = -sinx - (1(sinx) + x(cosx))$

$\frac{d^{2} y}{{d x}^{2}} = - sin x - sin x - x cos x$ $(d^2y)/(dx^2) = -sinx - sinx - xcosx$

$\frac{d^{2} y}{{d x}^{2}} = - 2 sin x - x cos x$ $(d^2y)/(dx^2) = -2sinx - xcosx$

Hopefully this helps!

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How do you determine the derivative of $x cos x$ $xcosx$ ?

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