(1)differentiates,x^x^10

Question

Question(2),compute each of the following double integral over the rectangles where R=(-2,-1)*(0,1),§x^2y^2+cos(paix)+sin(paiy)dA
qustion3:investigate the stationary point of f(x) if y=3x^2+y^3-3x^2-3y^2-2

Answer 1

pi not pai!!

d/dx u^v = v*u^(v-1)u' + lnu u^v v'
You have u=x and v=x^10

∫[-2,-1]∫[0,1] x^2y^2+cos(πx)+sin(πy) dy dx
= ∫[-2,-1] 1/3 x^2 y^2 + cos(πx)*y - 1/π cos(πy) [0,1] dx
= ∫[-2,-1] 1/3 x^2 + cos(πx) + 2/π dx
= 1/9 x^3 + 1/π sin(πx) + 2/π x [-2,-1]
= 7/9 + 2/π

Not sure I know what you mean on #3. The language is kind of strange.