`2sqrt(x) + sqrt(y) = 3` Find `(dy/dx)` by implicit differentiation.
- print Print
- list Cite
Expert Answers
hkj1385
| Certified Educator
calendarEducator since 2015
write264 answers
starTop subjects are Math and Science
Note:- 1) If y = x^n ; then dy/dx = n*x^(n-1) ; where n = real number
2) If y = k ; where 'k' = constant ; then dy/dx = 0
Now,
{2x^(1/2)} + y^(1/2) = 3
Differentiating both sides w.r.t 'x' we get
x^(-1/2) + (1/2){y^(-1/2)}*(dy/dx) = 0
or, dy/dx = -[2*x^(-1/2)]/[y^(-1/2)]
or, dy/dx = -2[x/y]^(-1/2) = -2*[y/x]^(1/2)
Related Questions
- Find dy/dx by implicit differentiation. e^(x/y) = 5x-y
- 1 Educator Answer
- Find dy/dx by implicit differentiation: tan(x-y) = y/(2+x^2)
- 1 Educator Answer
- `x e^y = x - y` Find `(dy/dx)` by implicit differentiation.
- 1 Educator Answer
- Find dy/dx by implicit differentiation. sqrt(5x+y) = 6+x^2y^2
- 1 Educator Answer
- `x^2 + xy - y^2 = 4` Find `(dy/dx)` by implicit differentiation.
- 1 Educator Answer
balajia | Student
`2sqrt(x)+sqrt(y)=3`
differentiating with respect to x.
`2(1/(2sqrt(x)))+(1/(2sqrt(y)))(dy/dx)=0`
`dy/dx=(-(2sqrt(y))/sqrt(x))`
Student Answers