@iwantcalculus, there's the "brute force" way, which is how you are proceeding, and there's a different way that involves implicit differentiation. What's another way to write the equation you're starting with.ehild said:
Absolutely. Posting an image of your work doesn't let us insert a comment at a particular location where you might have gone wrong.ehild said:
Implicit differentiation is a method used in calculus to find the derivative of an equation that is not explicitly expressed in terms of a single variable. It is commonly used when the equation contains both dependent and independent variables, making it difficult to solve for the derivative using traditional methods.
Inverse trigonometric functions are mathematical functions that undo the effects of trigonometric functions. They are commonly denoted with "arc" in front of the function symbol, such as arcsine (sin-1), arccosine (cos-1), and arctangent (tan-1).
When using implicit differentiation with inverse trig functions, we first substitute the inverse function for the variable in the equation. Then, we apply the chain rule to differentiate the inverse trig function. Finally, we solve for the derivative of the original equation by substituting the inverse trig function back in for the variable.
The chain rule is a rule in calculus that allows us to find the derivative of a composite function. It states that if a function f(x) is composed of two functions, g(x) and h(x), then the derivative of f(x) is equal to the derivative of g(x) multiplied by the derivative of h(x) with respect to x.
Some common mistakes when using implicit differentiation with inverse trig functions include forgetting to substitute the inverse function for the variable, not applying the chain rule correctly, and not solving for the derivative of the original equation correctly. It is important to carefully follow each step and double check your work to avoid these mistakes.