suchgreatheig said:Homework Statement
Use implicit differentiation to find dy/dx if y - sin(xy) = x^2.
Implicit differentiation is a mathematical technique used to find the derivative of a function that is not expressed explicitly in terms of one variable. It is commonly used to find the slope of a curve at a specific point.
Implicit differentiation is useful in situations where a function cannot be easily solved for one variable, such as when there are multiple variables or when the function is expressed implicitly. It allows us to find the derivative without having to manipulate the equation into explicit form.
Explicit differentiation involves finding the derivative of a function that is expressed explicitly in terms of one variable. Implicit differentiation, on the other hand, is used for functions that cannot be easily solved for one variable and therefore involves differentiating with respect to both variables.
The first step is to identify the variables in the equation and determine which one you are differentiating with respect to. Then, use the rules of differentiation, such as the product rule and chain rule, to find the derivative. Finally, solve for the derivative by isolating the variable of interest.
Implicit differentiation is most commonly used in applications involving curves and surfaces, such as in physics, economics, and engineering. It is also used in advanced calculus and differential equations courses.