- #1
tellmesomething
- 449
- 59
- Homework Statement
- ##\frac{1}{y} +\frac{1}{x} = \frac{1}{12}##. Find the rate of change of x with respect to time atx=5,y=1, if dy/dt=-1
- Relevant Equations
- Ok
I rearranged the equation and got
$$12x+12y=xy$$
Differentiating this I get
$$12\frac{dx}{dt} + 12\frac{dy}{dt} = x\frac{dy}{dt} + y\frac{dx}{dt}$$
Substituting the values I get
$$12\frac{dx}{dt} -12= -5+\frac{dx}{dt}$$
SO
$$\frac{dx}{dt}=\frac{7}{11}$$
But if I directly differentiate the given equation
##\frac{1}{y} +\frac{1}{x} = \frac{1}{12}##
I get
$$\frac{-1}{x²} \frac{dx}{dt}-\frac{1}{y²} \frac{dy}{dt}=0$$
And here if I substitute the values I get
dx/dt=25
Im not sure where I went wrong in the first method, I'm guessing the differentiation of d(xy)/dt is a little more complicated. Can someone help me out please?
$$12x+12y=xy$$
Differentiating this I get
$$12\frac{dx}{dt} + 12\frac{dy}{dt} = x\frac{dy}{dt} + y\frac{dx}{dt}$$
Substituting the values I get
$$12\frac{dx}{dt} -12= -5+\frac{dx}{dt}$$
SO
$$\frac{dx}{dt}=\frac{7}{11}$$
But if I directly differentiate the given equation
##\frac{1}{y} +\frac{1}{x} = \frac{1}{12}##
I get
$$\frac{-1}{x²} \frac{dx}{dt}-\frac{1}{y²} \frac{dy}{dt}=0$$
And here if I substitute the values I get
dx/dt=25
Im not sure where I went wrong in the first method, I'm guessing the differentiation of d(xy)/dt is a little more complicated. Can someone help me out please?