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How/when should I use the product rule for differentiation?

The product rule can be used to differentiate a function that is formed of the product of two other functions;

e.g f(x)=x2ex

the product rule is as follows; if f(x) is split up into u.v (in this case u would be x2 and v would be ex), the derivative of th whole function is (u.dv/dx) + (v.du/dx)

so in this case u=x2, following standard differentiation du/dx= 2x

v=ex, dv/dx=ex

u.dv/dx=x2ex

v.du/dx=2xex

so the whole function differentiated = ex(x2+2x)

 

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