Answer to: What is the derivative of x!? By signing up, you'll get thousands of step-by-step solutions to your homework questions. You can also ask...
For the expression or the function of the form with powers, we will apply the power rule of differentiation. Now it can be seen that the formula of the power rule is:ddx(xa)=a⋅xa−1, We have a contant term here asa. Answer and Explanation: ...
We are given a trigonometric function. The chain rule is used to find out the derivative of the given composite function. To solve this kind of problems, we'll use the chain rule. The chain rule states that: {eq}\dfrac{\ df(u)}{ \ dx} = \dfrac{\ df}{ \ du} \dfrac{\ du}{...
That is, the derivative of f(x) is the quotient of an infinitesimal change in y over an infinitesimal change in x. Put more precisely, it is exactly the limit of the change in y over the change in x over smaller and smaller changes in x. The “dx” and “dy” notation just captur...
Answer to: What is the derivative of \sec^{-1}(x + 2)^2 = \frac{2}{(x + 2) \sqrt{(x + 2) - 1}}? By signing up, you'll get thousands of...
$\dfrac{dy}{dx}=\dfrac{1}{{{x}^{2}}+1}$ Now, the second derivative of $\arctan $ can be directly calculated by the Quotient Rule formula. The formula of the Quotient Rule is give as, $f'\left( x \right)=\dfrac{g'\left( x \right)h\left( x \right)-h'\left( x \...
Discusses the problem with the definition of the dy/dx mathematical notation. Incompleteness of the definition; Ambiguity; Derivation of a new definition for dy/dx; Relation between the derived definition with the traditional definition of dy/dx; Use of the Leibnizian derivative.Thurston...
Find y' if y= ln( x^2 + y^2) I thought this was just a regular natural log derivative combined with the chain rule. So what I got was (2x + 2y)/ (x^2 +...
A differential represents a change in a function, while a derivative measures the rate of that change. Both are foundational concepts in calculus.
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