How can I solve the problem?
How to finddy/(dx) of the mentioned equation?
xsqrt(1+y)+ysqrt(1+x)=0
How to find
1 Answer
Dec 28, 2017
Explanation:
"differentiate "color(blue)"implicitly with respect to x"
"differentiate "xsqrt(1+y)" and "ysqrt(1+x)" using "
"the "color(blue)"product rule"
rArrx(1+y)^(1/2)+y(1+x)^(1/2)=0
rArr(x . 1/2(1+y)^(-1/2).dy/dx+(1+y)^(1/2))
+(y . 1/2(1+x)^(-1/2)+(1+x)^(1/2).dy/dx)=0
rArr1/2x(1+y)^(-1/2)dy/dx+(1+x)^(1/2)dy/dx
=-1/2y(1+x)^(-1/2)-(1+y)^(1/2)
rArrdy/dx(1/2x(1+y)^(-1/2)+(1+x)^(1/2))
=-1/2(y(1+x)^(-1/2)+2(1+y)^(1/2))
rArrdy/dx=-(cancel(1/2)(y(1+x)^(-1/2)+2(1+y)^(1/2)))/(cancel(1/2)(x(1+y)^(-1/2)+2(1+x)^(1/2))
color(white)(rArrdy/dx)=-(y/sqrt(1+x)+2sqrt(1+y))/(x/sqrt(1+y)+2sqrt(1+x))
