What is the derivative of #(4x)^3 * (2x)^6#?

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Answer 1 · 2016-11-01T20:06:53

#y'=36864x^8#

#y=(4x)^3(2x)^6#

#y=4^3 x^3*2^6 x^6#

#y=4096x^9#

#y'=36864x^8#

OR

#f=(4x)^3, g=(2x)^6#

#f'=3(4x)^2 *4, g'=6(2x)^5*2#

#y'=fg'+gf'#

#y'=12(4x)^3(2x^5)+12(4x)^2(2x)^6#

#y'=12*4^3x^3*2^5x^5+12*4^2x^2*2^6x^6#

#y'=24576x^8+12288x^8=36864x^8#