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

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

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

$y'=fg'+gf'$

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

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

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

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