Liquidxlax said:Homework Statement
m=a+b n=a2+b2
cepheid said:Wait, so are you saying that m = a + bn AND m = a2 + b2?
Liquidxlax said:no
m=a+b and n=a^2 +b^2
Liquidxlax said:(dm/db)a = 1 is that right?
Liquidxlax said:and
(db/dm)n
Liquidxlax said:m = b - sqrt(b2-n)
cepheid said:Okay.
Yeah.
This suggests that you want the function b(n,m), so you have to take what you have
solve it for b, and then differentiate that w.r.t. m, keeping n constant.
A partial derivative problem is a mathematical problem that involves finding the rate of change of a function with respect to one of its variables, while holding all other variables constant. It is a way to measure how much a function changes when only one variable is allowed to vary, while keeping all other variables fixed.
To solve a partial derivative problem, you will need to use the partial derivative formula, which involves taking the derivative of the function with respect to the variable of interest, while treating all other variables as constants. This will give you the partial derivative of the function. You may also need to use implicit differentiation or the chain rule, depending on the complexity of the problem.
Partial derivatives are commonly used in multivariable calculus to analyze the rate of change of a function with respect to one of its variables. They are also used in physics and engineering to model and solve problems involving multiple variables. In general, if you are dealing with a function that has multiple variables, you will likely need to use partial derivatives.
Partial derivatives have numerous real-world applications, especially in fields such as physics, economics, and engineering. For example, they can be used to analyze the rate of change of a chemical reaction, optimize production processes, or study the impact of variables on stock prices. They are also used in computer graphics to create 3D models and animations.
Yes, a partial derivative can be negative. This indicates that the function is decreasing in the direction of the variable being considered, while all other variables are held constant. It is important to pay attention to the sign of a partial derivative, as it can provide valuable information about the behavior of the function.