Find the differential of y in the function: y=x^3cosx ?

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1 Answer
Øko
Mar 4, 2018

#dy/dx=3x^2cos(x)-x^3sin(x)#

Explanation:

We want to find the derivative of

#y=x^3cos(x)#

Use the product rule, if #y=f*g#

then #dy/dx=f'*g+f*g'#, thus

  • #f=x^3=>f'=3x^2#
  • #g=cos(x)=>g'=-sin(x)#

By the product rule

#dy/dx=3x^2cos(x)-x^3sin(x)#

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