Calculadora de Derivada Parcial
Calcular derivadas parciais passo a passo
Esta calculadora online calculará a derivada parcial da função, com as etapas mostradas. Você pode especificar qualquer ordem de integração.
Solution
Your input: find $$$\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(81 x^{2} + y^{2}\right)$$$
First, find $$$\frac{\partial}{\partial l}\left(81 x^{2} + y^{2}\right)$$$
The derivative of a constant is 0:
$${\color{red}{\frac{\partial}{\partial l}\left(81 x^{2} + y^{2}\right)}}={\color{red}{\left(0\right)}}$$Thus, $$$\frac{\partial}{\partial l}\left(81 x^{2} + y^{2}\right)=0$$$
Next, $$$\frac{\partial^{2}}{\partial l \partial a}\left(81 x^{2} + y^{2}\right)=\frac{\partial}{\partial a} \left(\frac{\partial}{\partial l}\left(81 x^{2} + y^{2}\right) \right)=\frac{\partial}{\partial a}\left(0\right)$$$
The derivative of a constant is 0:
$${\color{red}{\frac{\partial}{\partial a}\left(0\right)}}={\color{red}{\left(0\right)}}$$Thus, $$$\frac{\partial}{\partial a}\left(0\right)=0$$$
Next, $$$\frac{\partial^{3}}{\partial l \partial a \partial m}\left(81 x^{2} + y^{2}\right)=\frac{\partial}{\partial m} \left(\frac{\partial^{2}}{\partial l \partial a}\left(81 x^{2} + y^{2}\right) \right)=\frac{\partial}{\partial m}\left(0\right)$$$
The derivative of a constant is 0:
$${\color{red}{\frac{\partial}{\partial m}\left(0\right)}}={\color{red}{\left(0\right)}}$$Thus, $$$\frac{\partial}{\partial m}\left(0\right)=0$$$
Next, $$$\frac{\partial^{4}}{\partial l \partial a \partial m \partial d}\left(81 x^{2} + y^{2}\right)=\frac{\partial}{\partial d} \left(\frac{\partial^{3}}{\partial l \partial a \partial m}\left(81 x^{2} + y^{2}\right) \right)=\frac{\partial}{\partial d}\left(0\right)$$$
The derivative of a constant is 0:
$${\color{red}{\frac{\partial}{\partial d}\left(0\right)}}={\color{red}{\left(0\right)}}$$Thus, $$$\frac{\partial}{\partial d}\left(0\right)=0$$$
Next, $$$\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(81 x^{2} + y^{2}\right)=\frac{\partial}{\partial a} \left(\frac{\partial^{4}}{\partial l \partial a \partial m \partial d}\left(81 x^{2} + y^{2}\right) \right)=\frac{\partial}{\partial a}\left(0\right)$$$
The derivative of a constant is 0:
$${\color{red}{\frac{\partial}{\partial a}\left(0\right)}}={\color{red}{\left(0\right)}}$$Thus, $$$\frac{\partial}{\partial a}\left(0\right)=0$$$
Therefore, $$$\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(81 x^{2} + y^{2}\right)=0$$$
Answer: $$$\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(81 x^{2} + y^{2}\right)=0$$$