Kalkulator Turunan Parsial

Your input: find $$$\frac{\partial}{\partial x}\left(x^{2} y^{2}\right)$$$

Apply the constant multiple rule $$$\frac{\partial}{\partial x} \left(c \cdot f \right)=c \cdot \frac{\partial}{\partial x} \left(f \right)$$$ with $$$c=y^{2}$$$ and $$$f=x^{2}$$$:

$${\color{red}{\frac{\partial}{\partial x}\left(x^{2} y^{2}\right)}}={\color{red}{y^{2} \frac{\partial}{\partial x}\left(x^{2}\right)}}$$

Apply the power rule $$$\frac{\partial}{\partial x} \left(x^{n} \right)=n\cdot x^{-1+n}$$$ with $$$n=2$$$:

$$y^{2} {\color{red}{\frac{\partial}{\partial x}\left(x^{2}\right)}}=y^{2} {\color{red}{\left(2 x^{-1 + 2}\right)}}=2 x y^{2}$$

Thus, $$$\frac{\partial}{\partial x}\left(x^{2} y^{2}\right)=2 x y^{2}$$$

Answer: $$$\frac{\partial}{\partial x}\left(x^{2} y^{2}\right)=2 x y^{2}$$$