Find an equation of the tangent line to the curve (x^2)(e^y)+(ye^x)=4 at the point (2,0).

Question

I think you're supposed to use implicit differentiation.

Answer 1

"Solution:Given (x^2)(e^y)+(ye^x)=4

differentiating

=> 2x*e^y+x²e^yy'+ye^x+e^xy'=0

substitute

x = 2and y = 0

=>(4+e²)y'(x)+4=0

=>slope m= y'(x)= -4/(4+e²)

=>y-y1=m(x-x1)

=>y-0=-4/(4+e²)(x-2)

=>equation of the tangent line

y=-4x/(4+e²)+8/(4+e²)"

Tangent Tables

Sine Cosine and Tangent are the trigonometric ratios.They are defined as the ratio of sides of a triange.For every angle we have a sine cosine and tangent values.It is arelation between angle and sides if a triangle. If the angle is in radian we can convert it to degree using , radian=degree*pi/180,pi=3.1428. Here we have sine cosine and tangent values for angles 0 to 90.