2x*9x^y9=

3 answers

is it 18x^y^9+1??
this is my work

{(x, y) element R^2 : x>0 or (x = 0 and y>0)}

(d)/(dx)(2 x×9 x^(y^9)) = 18 (y^9 + 1) x^(y^9)

18 x^(1 + y^9) dx = (18 x^(y^9 + 2))/(y^9 + 2) +
quite a difference in your posts.
2x * 9x^(y^9))
= 18x^(y^9+1)

Now, taking the derivative of u^v is a combination of

d/dx a^v = lna a^v dv/dx
d/dx u^n = n u^(n-1) du/dx

d/dx u^v = v u^(v-1) u' + lnu u^v v'

Since we have u=x, and v=y^9+1, taking d/dx, we get

(y^9+1) x^(y^9) + lnx x^(y^9+1) y'

Not sure what the rest of the question is...