Calculadora de derivadas parciales
Calcular derivadas parciales paso a paso
Esta calculadora en línea calculará la derivada parcial de la función, con los pasos que se muestran. Puede especificar cualquier orden de integración.
Solution
Your input: find $$$\frac{\partial}{\partial x}\left(3 x + 4 y\right)$$$
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}{\frac{\partial}{\partial x}\left(3 x + 4 y\right)}}={\color{red}{\left(\frac{\partial}{\partial x}\left(3 x\right) + \frac{\partial}{\partial x}\left(4 y\right)\right)}}$$The derivative of a constant is 0:
$${\color{red}{\frac{\partial}{\partial x}\left(4 y\right)}} + \frac{\partial}{\partial x}\left(3 x\right)={\color{red}{\left(0\right)}} + \frac{\partial}{\partial x}\left(3 x\right)$$Apply the constant multiple rule $$$\frac{\partial}{\partial x} \left(c \cdot f \right)=c \cdot \frac{\partial}{\partial x} \left(f \right)$$$ with $$$c=3$$$ and $$$f=x$$$:
$${\color{red}{\frac{\partial}{\partial x}\left(3 x\right)}}={\color{red}{\left(3 \frac{\partial}{\partial x}\left(x\right)\right)}}$$Apply the power rule $$$\frac{\partial}{\partial x} \left(x^{n} \right)=n\cdot x^{-1+n}$$$ with $$$n=1$$$, in other words $$$\frac{\partial}{\partial x} \left(x \right)=1$$$:
$$3 {\color{red}{\frac{\partial}{\partial x}\left(x\right)}}=3 {\color{red}{1}}$$Thus, $$$\frac{\partial}{\partial x}\left(3 x + 4 y\right)=3$$$
Answer: $$$\frac{\partial}{\partial x}\left(3 x + 4 y\right)=3$$$