2015年4月7日 · color(red)(xy=x+y Transposing x to the Left Hand Side will give us xy-x=y x*(y-1) = y (x was a common ...

2016年7月1日 · How do you use implicit differentiation to find #y'# for #sin(xy) = 1#? How do you find the second derivative by implicit differentiation on #x^3y^3=8# ? What is the derivative of …

2017年1月20日 · (dy)/(dx)=-y^2/x^2 Using the quotient rule d/(dx)(u/v)=(vu'-uv')/v^2 d/(dx)((xy)/(x+y)=1) ((x+y)(y+xy')-(xy(1+y')))/(x+y)^2=0 ie.(x+y)(y+xy')-xy(1+y')=0 cancel(xy)+x ...

2016年7月22日 · (x+y)(x-y)=x^2-y^2 To simplify (x+y)(x-y) we use distributive property of number systems. Let us treat (x+y) as a single number and distribute it over (x-y). This makes (x+y)(x …

2017年2月28日 · x-y=color(green)(18) Given [1]color(white)("XXX")xy=144 [2]color(white)("XXX")x+y=30color(white)("X")rarrcolor(white)("X")y=30-x Substituting (30-x) for …

2015年5月17日 · #xy + x - y -1# We factor this expression by making groups of 2 terms #= (xy + x) + (-y -1)# Now we take the common factors out from each group

2015年4月26日 · You have to use the implicit function theorem (aka the Dini's theorem) The implicit equation is F(x,y)=1-x-xy+y=0, F is a smooth function (it's a polynomial), so we can use …

2017年3月17日 · See a couple of solution processes below: This is an example of the perfect square. The formula for this is: (a + b)(a + b) = a^2 + 2ab + b^2 Substituting x for a and y for b …

2017年2月5日 · dy/dx = e^(-xy)((1-xy)/(1+xy)) Start from the equation: e^(xy) = y/x As the first member is always positive, so is the second, and we can take the logarithm of both sides: xy = …

Implicit differentiation allows differentiating complex functions without first rewriting in terms of a single variable. For example, instead of first solving for y=f(x), implicit differentiation allows …