## Answer in 60

### Input interpretation

### Result

### Alternate form

### Alternate form assuming x and y are positive

**Key moments in video**

From 01:36 — What are the steps?

From 02:03 — How to differentiate a term with y

From 05:19 — Differentiating both sides of the equation

From 05:42 — Solve for dy / dx

From 10:54 — How to only have dx terms on 1 side

From 12:05 — Factor out the dx from both terms

From 13:11 — Warnings about implicit differentiation

**Key moments in video**

From 02:35 — 2 Given the Equation X Cubed Plus 4 Xy Plus Y Squared Is Equal to 13 Find Dy Dx

From 05:47 — 3 Find Dy / Dx by Implicit Differentiation

From 09:42 — Find a Second Derivative

From 12:24 — Eliminate the Complex Fraction

## Related querie

### What is implicit differentiation formula?

In implicit differentiation, we **differentiate each side of an equation with two variables (usually x and y) by treating one of the variables as a function of the other**. This calls for using the chain rule. Let's differentiate x 2 + y 2 = 1 x^2+y^2=1 x2+y2=1x, squared, plus, y, squared, equals, 1 for example.

### What is implicit differentiation give an example?

For example, **xÂ²+yÂ²=1**. Implicit differentiation helps us find â€‹dy/dx even for relationships like that. This is done using the chain â€‹rule, and viewing y as an implicit function of x. For example, according to the chain rule, the derivative of yÂ² would be 2yâ‹…(dy/dx).

### What is an implicit differential equation?

An ordinary differential equation is called implicit **when the derivative of the dependent variable, , can not be isolated and moved to the other side of the equal sign**.

### How does implicit differentiation work?

In implicit differentiation, **we differentiate each side of an equation with two variables (usually x and y) by treating one of the variables as a function of the other**. This calls for using the chain rule.

### What is the implicit differentiation of XY?

Implicit differentiation of (x-y)**Â²=x+y-1**.

### How do you explain implicit differentiation?

In implicit differentiation, we **differentiate each side of an equation with two variables (usually x and y) by treating one of the variables as a function of the other**. This calls for using the chain rule. Let's differentiate x 2 + y 2 = 1 x^2+y^2=1 x2+y2=1x, squared, plus, y, squared, equals, 1 for example.

### What is implicit and explicit?

Explicit describes something that is very clear and without vagueness or ambiguity. Implicit often functions as the opposite, referring to something that is understood, but not described clearly or directly, and often using implication or assumption.

### Whats the difference between implicit and differentiation?

**The "implicit" does not refer to the act of differentiation, but to the function being differentiated**. Implicit differentiation means "differentiating an implicitly defined function". This is a simple equation of two variables, but you can understand it another way.

### What is the first step of implicit differentiation?

Luckily, the first step of implicit differentiation is its easiest one. Simply **differentiate the x terms and constants on both sides of the equation according to normal (explicit) differentiation rules to start off**. Ignore the y terms for now.

### What is the formula of XY?

Answer: The formula is **(x-y)Â³=xÂ³-3xÂ²y+3xyÂ²-yÂ³**.