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Partial Derivative is nothing but the derivative of a function of multiple variables with respect to one variable and all other variables are kept constant. No need to get panic to solve the partial derivative of an expression. You can simply go through the following mentioned steps and use them to get the partial derivative easily.
Question: Solve ∂2/∂x [4x2y3+x2] using partial differentiation method?
∂2/∂x [4x2y3+x2]= ∂/∂x[∂/∂x(4x2y3+x2)
Let us take function f=4x2y3+x2
We can also write ∂2/∂x [4x2y3+x2] = ∂/∂x(∂f/∂x)
Consider y as constant
∂2/∂x [4x2y3+x2 = 8y3+2 = 2(4y3+1)
Try to solve the partial derivative of a function manually by using the above simple steps or else make use of the Onlinecalculator.guru provided handy calculator tool to get the result in split second.
1. What is the difference between a derivative and a partial derivative?
Derivative isa applied to a function that has only one independent variable. Partial derivative is applied to functions that have more than one independent variable.
2. Why are partial derivatives used?
Partial differentiation is used to differentiate mathematical functions having more than one variable in them.
3. Can you integrate a partial derivative?
Yes, we can integrate the function f(x,y) with respect to x, a process refer as partial integration. Suppose for the function f(x,y) do the partial derivative with respect to y and integrate f(x,y) with respect to y.
4. Does order of partial derivatives matter?
The order of partial differentiation does not matter for any function. We may first differentiate with respect to one variable and then with respect to another.