Search2. Find the equation of the tangent line onx2+ sin y – ry? = 4 at (2,0).

NOTE: Refresh your page if you can't see any equations. . take derivative

Answered: Find the equation of the tangent line…

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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Step 1

NOTE: Refresh your page if you can't see any equations.

$x^2+\sin \left(y\right)-xy^2=4$

$x^2+\sin \left(y\right)-xy^2-4=0$

take derivative

$\frac{d}{dx}\left(x^2+\sin \left(y\right)-xy^2-4\right)=0$

$\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(\sin \left(y\right)\right)-\frac{d}{dx}\left(xy^2\right)-\frac{d}{dx}\left(4\right)=0$

$2x+\cos \left(y\right)\cdot \frac{dy}{dx}-\left(y^2+2xy\cdot \frac{dy}{dx}\right)-0=0$

$2x+\cos \left(y\right)\cdot \frac{dy}{dx}-y^2-2xy\cdot \frac{dy}{dx}=0$

$\cos \left(y\right)\cdot \frac{dy}{dx}-2xy\cdot \frac{dy}{dx}=-2x+y^2$

$\left(\cos \left(y\right)-2xy\right)\frac{dy}{dx}=-2x+y^2$

$\frac{dy}{dx}=\frac{-2x+y^2}{\cos \left(y\right)-2xy}$

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