Ratkaise (1+xy)^frac{sinx{x^2+y^2}}

$$( 1 + x y ) ^ { \frac { \sin x } { x ^ { 2 } + y ^ { 2 } } }$$

Laske

$$\left(xy+1\right)^{\frac{\sin(x)}{x^{2}+y^{2}}}$$

Derivoi muuttujan x suhteen

$$\frac{\left(xy^{3}\cos(x)\ln(xy+1)+yx^{3}\cos(x)\ln(xy+1)+x^{2}\cos(x)\ln(xy+1)+y^{2}\cos(x)\ln(xy+1)-2yx^{2}\sin(x)\ln(xy+1)+y^{3}\sin(x)-2x\sin(x)\ln(xy+1)+yx^{2}\sin(x)\right)\left(xy+1\right)^{\frac{\sin(x)}{x^{2}+y^{2}}-1}}{\left(x^{2}+y^{2}\right)^{2}}$$