good day, I have been asked to differentiate the following:
$x^{395} * (1-2x)^{605}$
I have applied chain rule to $(1-2x)^{605}$ which gives me $-1210(1 - 2x)^{604}$ and the I apply product rule to the original function. the answer I get is:
$395(1−2x)^{605} * x^{394} − 1210(1−2x)^{604} * x^{395}$
but this is not the correct answer as I have been given it. it is:
$x^{394}*(1 − 2x)^{604} * (395 − 2000x)$ and I have no idea why?
any suggestions as i know that my differentiation is correct?
applying the product and the chain rule we get $$395x^{394}(1-2x)^{605}+x^{395}(1-2x)^{604}\cdot 605\cdot (-2)$$ this can be simplified the result should be $$-5\,{x}^{394} \left( -1+2\,x \right) ^{604} \left( -79+400\,x \right) $$ or $$x^{394}(-1+2x)^{604}(395-2000x)$$