Dough said:i am not sure what else y have to do to get the answer, i wrote that out as well as
-1 = x^2 + 3x -5
solved and got x = 1 or -3...
but what else?
dy/dx = f'(x^2 + 3x - 5)(2x + 3)
Derivatives of composite functions are a type of derivative that involves taking the derivative of a function that is composed of two or more other functions. In other words, the inner function is substituted into the outer function, and then the derivative is taken.
To find the derivative of a composite function, you can use the chain rule, which states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function.
Yes, an example of a composite function is f(x) = sin(3x), which can be rewritten as f(x) = sin(u) where u = 3x. The derivative of this function is f'(x) = 3cos(3x).
The purpose of finding derivatives of composite functions is to analyze the rate of change of a function that is composed of multiple functions. This can be useful in many areas of science, such as physics, engineering, and economics.
Yes, there are a few special cases when finding derivatives of composite functions. For example, when the inner function is a constant, the derivative is simply the derivative of the outer function. Additionally, when the inner function is a linear function, the chain rule can be simplified.