Find the derivative of the implicit function {eq}F(x,y) = x^2 + y^2 + (xy)^{1/2} = 0 {/eq} Derivative of Implicit Function: For finding the derivative of the implicit function, we are going to use the implicit differentiation technique. Initially, we hav...
Implicit differentiationis the process of differentiating animplicit function.An implicit function is a function that can be expressed as f(x, y) = 0. i.e., it cannot be easily solved for 'y' (or) it cannot be easily got into the form of y = f(x). Let us consider an example of...
Derivatives of Inverse Trigonometric Functions View Solution Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Rajasthan ...
For any implicit function f=g(x)h(y) its derivative will be given by, D(f)=g(x) [h′(y)y′(x) ]+h(y) [g′(x) ] (where g is a function of x only and h is a function of y only, also y is a function of x) ...
f' represents the derivative of a function f of one argument. Derivative[n1, n2, ...][f] is the general form, representing a function obtained from f by differentiating n1 times with respect to the first argument, n2 times with respect to the second argu
In the framework of the theory of normal coderivative for multifunctions, new implicit function theorems are obtained. The main tools of the proofs are the Ekeland variational principle, a nonsmooth version of Fermat's rule, a sum rule, and the differential estimate for marginal functions ...
Implicit differentiation Taylor's theorem Related rates IdentitiesIn calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point. For example...
Examples collapse all Functional Derivative with Respect to Single Function Copy Code Copy Command Find the functional derivative of the functional S[y]=∫aby(x)sin(y(x))dx with respect to the function y, where the integrand is f[y(x)]=y(x)sin(y(x)). Declare y(x) as a symbolic ...
3. Implicit Derivative Implicit differentiation is used when a function is defined implicitly rather than explicitly. It allows you to find derivatives without solving for one variable in terms of others, which is particularly useful for equations where the dependent variable is intertwined with the ...
Calculate directional derivatives of multivariable functions with detailed step-by-step solutions!Directional Derivative Calculator Compute the Directional Derivative: Try the following examples: [Example 1] [Example 2] [Example 3] [Example 4] [Example 5] Function f(x,y): Variables: Point (x0...