Implicit Differentiation calculator is a free online calculator that displays the derivative of the given function with respect to the variable.
About Implicit Differentiation Calculator
Inputs
- Implicit form function
Steps To Use Calculators
The following steps show how to use the implicit Differentiation calculator
- Type the equation into the appropriate input field.
- To receive the derivative of a function, click the “Submit” button.
- In the new window, the derivative will be displayed.
Outputs
- Input Interpretation
- Results
Implicit Differentiation
In Calculus, a function can be in implicit form at times and it signifies that the function is expressed in both x and y terms. The implicit form of a parabola equation for example is \( y2 = – 4ax\). The process of determining the derivative of these implicit functions is called implicit differentiation.
Steps
- Firstly, you need to differentiate the function with respect to x.
- While differentiating y terms you get dy/dx.
- Then, collect all dy/dx on one side.
- Lastly, solve for dy/dx.
Example Problems
Question 1: Find y′ for xy=1?
Solution: Given implicit function => xy =1
Differentiating with respect to x.
=> d(xy)/dx = d(1)/dx
Using product rule, we differentiate the first term
=> 1.y + x.(dy/dx) = 0
We know that y′ = dy/dx
y + xy′ = 0
=> y′ = -y/x
From the equation we know that y = 1/x, substituting this in the implicit differential, we get
=> y′ = 1/x2
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