## 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.

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Enter the order of integration:

Hint: type x^2,y to calculate (partial^3 f)/(partial x^2 partial y), or enter x,y^2,x to find (partial^4 f)/(partial x partial y^2 partial x).

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### Solution

Your input: find $\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(3 x + 4 y\right)$

### First, find $\frac{\partial}{\partial l}\left(3 x + 4 y\right)$

The derivative of a constant is 0:

$${\color{red}{\frac{\partial}{\partial l}\left(3 x + 4 y\right)}}={\color{red}{\left(0\right)}}$$

Thus, $\frac{\partial}{\partial l}\left(3 x + 4 y\right)=0$

### Next, $\frac{\partial^{2}}{\partial l \partial a}\left(3 x + 4 y\right)=\frac{\partial}{\partial a} \left(\frac{\partial}{\partial l}\left(3 x + 4 y\right) \right)=\frac{\partial}{\partial a}\left(0\right)$

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, $\frac{\partial^{3}}{\partial l \partial a \partial m}\left(3 x + 4 y\right)=\frac{\partial}{\partial m} \left(\frac{\partial^{2}}{\partial l \partial a}\left(3 x + 4 y\right) \right)=\frac{\partial}{\partial m}\left(0\right)$

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, $\frac{\partial^{4}}{\partial l \partial a \partial m \partial d}\left(3 x + 4 y\right)=\frac{\partial}{\partial d} \left(\frac{\partial^{3}}{\partial l \partial a \partial m}\left(3 x + 4 y\right) \right)=\frac{\partial}{\partial d}\left(0\right)$

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, $\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(3 x + 4 y\right)=\frac{\partial}{\partial a} \left(\frac{\partial^{4}}{\partial l \partial a \partial m \partial d}\left(3 x + 4 y\right) \right)=\frac{\partial}{\partial a}\left(0\right)$

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, $\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(3 x + 4 y\right)=0$

Answer: $\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(3 x + 4 y\right)=0$