Learn about differentiability. Understand how to tell if a function is differentiable and when it isn't and see a comparison of differentiable vs...
The derivative must exist for every point in the domain, otherwise the function is not differentiable. This might happen when you have a hole in the graph: if there’s a hole, there’s no slope (there’s a dropoff!).See: Differentiable vs. Non Differentiable Functions.Types of Functions:...
Baier, R., Farkhi, E., Roshchina, V.: The directed and Rubinov subdifferentials of quasidifferentiable functions. Part II: calculus. Nonlinear Anal. 75 (3), 1058–1073 (2012). Special Issue on Variational Analysis and Its Applications...
Product rule in calculus is a method to find the derivative or differentiation of a function given in the form of the product of two differentiable functions. That means, we can apply the product rule, or the Leibniz rule, to find the derivative of a function of the form given as: f(x...
The quotient rule, a rule used in calculus, determines the derivative of twodifferentiablefunctions in the form of a ratio. Simply put, the quotient rule is used when there is a need to derive one differentiable function being divided by a second differentiable function. Take a look at the ...
Let f(x) be a differentiable function. Consider the curve y=f(x).Let P(c,f(c)) be a point on the curve y=f(x) and let Q(c+h,f(c+h)) be a neighbouring point on the same curve. Then,Slope of chord, PQ=tan∠QPN=QNPN∴PQ=f(c+h)–f(c)h...
The derivative of constant times a function is the constant times the derivative of the function. If c is a constant and f is a differentiable function, then, (d/dx) [c f(x)] = c (d/dx) [f(x)] Constant Multiple Rule Proof When new functions are formed from old functions by mult...
For a function to be differentiable, it has to be continuous. All polynomials are continuous. The functions are NOT continuous at vertical asymptotes. The functions are NOT continuous at holes.☛ Related Topics:Here are some topics that you may be interested in while studying continuous functions...
A critical point is a point where the function is either not differentiable or its derivative is zero, whereas an asymptote is a line or curve that a function approaches, but never touches or crosses. How do you find the critical point of two variable functions?
closed interval [a,b] and differentiable on the open interval (a,b). Then there exists a value a<c