Question

What is the answer to this

Answer 1

Refer to the photo attached.

Answer 2

`\textrm {D. The derivative is }\frac{x^(3)\cdot(\boldsymbol{9x^(8)})-x^(9)\cdot(\boldsymbol{3x^(2)})}{x^(6)}`

Explanation:

Given

`f(x) = (u(x))/(v(x))`

the derivative of f(x) wrt x is

`f'(x) = (u'(x)v(x) - u(x)v'(x))/([v(x)]^2)`

`u(x) =x^9 \;so \; u'(x) = 9x^8`

`v(x) = x^3 , v'(x) = 3x^2\\\\\[v(x)\]^2 = [x^3]^2 = x^6`

Putting all these together we get

`f'(x)=y'=\frac{x^(3)\cdot(\boldsymbol{9x^(8)})-x^(9)\cdot(\boldsymbol{3x^(2)})}{x^(6)}`

Missing entries are in bold