The chain rule is a rule in calculus used to compute thederivativeof a composite function, which is a function made up of other functions. Simple Example of the Chain Rule: Imagine you have two functions: f(x)=x(squared) (a function that squares its input) g(x)=2x+3 (a function th...
Definition/Summary The chain rule is an elementary rule of calculus, but it can be understood without any knowledge of calculus: If a depends on b...
FAQ: What is the Chain Rule for Integration? What is the Whitman 8.7.18 chain rule? The Whitman 8.7.18 chain rule is a mathematical concept used in calculus to find the derivative of a composite function. It is named after mathematician George Whitman, who first introduced it in 1878. ...
In calculus, the u-substitution method is also called the change of variable method. This is the reverse phenomenon of the chain rule. It is used to find out the integrals and antiderivatives as well. For example: {eq}\begin{align*} \int {f\left( {g(x)} ...
Example 1:Let f(y) = y2and g(y) = ey. Use thechain rulein calculus to calculate h′(y) where h(y) = f(g(y)). Solution: Given, f(y) = y2and g(y) = ey. First derivative of above functions are f'(y) = 2y and g'(y) = ey ...
What is a Derivative? In calculus, a derivative measures how a function changes as its input changes. It tells you the rate of change or the slope of the function at any given point. If you imagine a graph of a function (e.g., a line or a curve), the derivative at any point te...
The antiderivative rules in calculus are basic rules that are used to find the antiderivatives of different combinations of functions.
What is the derivative of this function? g(x) = -500/x, x is not equal to 0. What is the derivative of csc^{-1}(x^{12} + 1) What is a derivative of \frac{-2x}{(x^2 - 1)^2}? In calculus, what is the derivative of x^2 + 2x + 3?
There isn't too much you can say generally about the relationship between these two functions. In general, they will behave very differently. Using calculus, we can say the following by the chain rule: the derivative of F(1/x) is F'(1/x)*(-1/x^2). Upvote • 0 Down...
the Product Rule: Integration by Parts Higher Order Approximations, Part 2: Taylor's Theorem Excursion into Complex Numbers and the Euler Identity Readership: Undergraduates, high school students, instructors and teachers, and scientifically literate readers with special interest in calculus and analysis....