Question

Oblicz pochodną względem zmiennej x:
[tex]g(x,y) = \sqrt{cos^{3}(4xy^{2}) } + x+ 2y[/tex]

Answer 1

[tex]g'_x(x,y)=\dfrac{1}{2\sqrt{\cos^3(4xy^2)}}\cdot 3\cos^2(4xy^2)\cdot (-\sin (4xy^2))\cdot 4y^2+1=\\\\=-\dfrac{6y^2\sin(4xy^2)\cos^2(4xy^2)}{\sqrt{\cos^3(4xy^2)}}+1[/tex]