Question

How do I find the derivative of `x^8*ln(x)`?

Answer 1

`x^7(1+8lnx)`

Explanation:

differentiate using the `color(blue)"product rule"`

`" If " f(x)=g(x).h(x)" then"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(f'(x)=g(x).h'(x)+h(x).g'(x))color(white)(2/2)|)))`

here `g(x)=x^8rArrg'(x)=8x^7`

and `h(x)=lnxrArrh'(x)=1/x`

`rArrf'(x)=(x^8 xx1/x)+(lnx xx8x^7)`

`=x^7+8x^7lnx=x^7(1+8lnx)`