Mathematics | Senioritis

John Rhodes
June 21, 2023
Calculus

Mastering The Arctan Function: Definition, Properties, And Examples Of Inverse Tangent Function

arctan(x) 1/(1+x^2) The function arctan(x), also known as the inverse tangent function or the arc tangent function, is the inverse of the tangent function. It is defined...

John Rhodes
June 21, 2023
Calculus

How To Find The Derivative Of A Function: Definition, Formula, And Example

What is the formula for definition of a derivative? Lim h->0 (f(x+h)-f(x))/h The formula for the definition of a derivative is: f'(x) = lim h→0 [f(x+h) –...

John Rhodes
June 21, 2023
Calculus

The Differential Quotient And Difference Quotient Formulas For Computing Derivatives.

What is the alternative form of a derivative? Lim x->a (f(x)-f(a))/x-a The alternative form of a derivative is known as the differential quotient or a difference quotient....

John Rhodes
June 21, 2023
Calculus

Mastering Vector Derivatives: Differentiating Dot And Cross Products

What is the derivative of (u•v) (u’•v)+(u•v’) The derivative of (u・v), where u and v are vectors, depends on whether we are taking the dot product or...

John Rhodes
June 21, 2023
Calculus

Master The Quotient Rule For Derivatives: A Comprehensive Guide For Math Enthusiasts

What is the derivative of [u/v] (v•u’-v’•u)/v^2 To find the derivative of the quotient of two functions u(x) and v(x), we can use the quotient rule. The...

John Rhodes
June 21, 2023
Calculus

Master The Derivative Of Ln(U): A Comprehensive Guide For Differentiable Functions

What is the derivative of [ln u] u’/u The derivative of ln(u) is equal to 1/u times the derivative of u: $$\frac{d}{dx}(\ln u) = \frac{1}{u}\frac{du}{dx}$$ This can...

John Rhodes
June 21, 2023
Calculus

Mastering Calculus: The Exponential Chain Rule For Derivatives Of E^U

What is the derivative of [e^u] e^u•u’ The derivative of [e^u] with respect to u is simply [e^u]. This is due to the property of exponential functions...

John Rhodes
June 21, 2023
Calculus

Floor Function And Derivatives: The Case Of [Sin X]

What is the derivative [sin x] Cos x The derivative of [sin x], where [ ] represents the floor function or greatest integer function, is not defined...