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Calculadora de derivadas parciales

Calcula derivadas parciales paso a paso

Esta calculadora en línea calculará la derivada parcial de la función, mostrando los pasos. Puede especificar cualquier orden de derivación.

Enter a function:

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 $$$\frac{\partial}{\partial x}\left(x y^{2} z^{3}\right)$$$

Apply the constant multiple rule $$$\frac{\partial}{\partial x} \left(c \cdot f \right)=c \cdot \frac{\partial}{\partial x} \left(f \right)$$$ with $$$c=y^{2} z^{3}$$$ and $$$f=x$$$:

$${\color{red}{\frac{\partial}{\partial x}\left(x y^{2} z^{3}\right)}}={\color{red}{y^{2} z^{3} \frac{\partial}{\partial x}\left(x\right)}}$$

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

$$y^{2} z^{3} {\color{red}{\frac{\partial}{\partial x}\left(x\right)}}=y^{2} z^{3} {\color{red}{1}}$$

Thus, $$$\frac{\partial}{\partial x}\left(x y^{2} z^{3}\right)=y^{2} z^{3}$$$

Answer: $$$\frac{\partial}{\partial x}\left(x y^{2} z^{3}\right)=y^{2} z^{3}$$$


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