How do you implicitly differentiate: sqrt(xy)=x^2y+1

1 answer:

3 0

Implicit expression refers to equation that are not strictly expressed in terms of y and x separately. In this case, the derivative of expression
sqrt(xy)=x^2y+1 is

sqrt x * 0.5 y ^-0.5 dy + sqrt y * 0.5 x ^-0.5 dx= x^2 dy + 2xy dx
dy (x^2 - 0.5 (x/y) ^0.5) = dx (2xy - 0.5 (y/x)^0.5)
dy/dx = (2xy - 0.5 (y/x)^0.5) / (x^2 - 0.5 (x/y) ^0.5)

You might be interested in

Is 0.35 l greater than 300 ml

muminat

Yes 0.35 L is greater than 300 ml

4 0

3 years ago

How do you find vertical, horizontal and oblique asymptotes for f(x) = (5x-15 )/ (2x 14)?

Andrei [34K]

For vertical asymptotes, find the values which make the function indetermine in this case x=-7,so this is the only vertical asymptote.
For horizontal asymptotes, find the limit when x tends to infinity:
=(5x/x-15/x)/(2x/x+14/x) = 5/2, this is the horizontal asymptote y=5/2
For obliques, you have to meet the degree of the numerator is exactly a greater degree than the denominator, in this case they are the same degree so no oblique asymptote.

6 0

3 years ago

Please help me Please please please help me

inn [45]

It’s because that ❣️ is 1000

4 0

4 years ago

Read 2 more answers

How does the graph of g(x) = (x + 4)^3 − 6 compare to the parent function f(x) = x^3?

ANTONII [103]

Answer:

D) g(x) is shifted 4 units to the left and 6 units down