Answer to: Find dy/dx by implicit differentiation. y = \sin xy By signing up, you'll get thousands of step-by-step solutions to your homework...
cos x (1 + sin y) + sin x (cos y) y' = -sin(xy) (y + xy') cos x (1 + sin y) + sin x (cos y) y' = -y sin(xy) - [x sin(xy)]y' cos x (1 + sin y) + [sin x cos y + x sin(xy)] y' = -y sin(xy) [sin x cos y + x sin(xy)] ...
we differentiated both sides with respect to x by considering y as a function of x, and this type of differentiation is called implicit differentiation. But for some functions like xy + sin (xy) = 0, writing it as an explicit
Find dy/dx using implicit differentiation: x^2y^2 + x sin y = 1 Find \frac{dy}{dx} by implicit differentiation. (\cos \pi x + \sin \pi y)^8 = 55 \frac{dy}{dx} = Find \frac{dy}{dx} by implicit differentiation. { 1. x^4 + y^5 = 9\\ 2. 4x^2 + 9xy ...
Find {eq}\dfrac{dy}{dx} {/eq} by implicit differentiation. {eq}\sin xy = x^2 - 3 {/eq} Implicit Differentiation: Conisder a function {eq}f(x,y)=constant {/eq} to be differentiated with respect to {eq}x {/eq}. The method that is applied to evaluate the derivative is impli...
Implicit Differentiation: f′(y)y′ Answer and Explanation:1 cos(xy)=x2+2y Differentiating with respect to x on both sides −sin(xy)[y+xdydx]=2x+2dydx {eq}-y\s... Learn more about this topic: Implicit Differentiation Technique, Formula & Examples ...
1、Implicit DifferentiationObjective: To find derivatives of functions that we cannot solve for y.How to do it ?By now, it should be easy for you to take the derivative of an equation such as xxy735If youre given an equation such as , you can still figure out the derivative by taking ...
For example, the equation y−x2=1y−x2=1 defines the function y=x2+1y=x2+1 implicitly. Implicit differentiation allows us to find slopes of tangents to curves that are clearly not functions (they fail the vertical line test). We are using the idea that portions of yy are ...
(x) such that the given equation is satisfied. The technique ofimplicit differentiationallows you to find the derivative ofywith respect toxwithout having to solve the given equation fory. The chain rule must be used whenever the functionyis being differentiated because of our assumption thatymay...
4 cos (xy) = 9x + 5y {eq}\frac{dy}{dx} = {/eq} Implicit Differentiation: We have to find the derivative of the given function. We will differentiate the given function with respect to x and use implicit differentiation to get the desired result. Answer and Explanati...