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teng125
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f(x,y)=2y / (y+cos x) .Find partial derivative w.r.t x
can someone teach me how to do this pls
thanx
can someone teach me how to do this pls
thanx
Uhmm, nope. The red-highlighted part is wrong. It should read uv', i.e the whole formula is:teng125 said:the formula is it vu'-u'v/(v^2) ??
A partial derivative is a mathematical concept that measures the rate of change of a function with respect to one of its variables, holding all other variables constant. In other words, it tells us how much a function changes when we change one of its input variables while keeping the other variables fixed.
To find the partial derivative of a function, we use the notation fx or ∂f/∂x, where x is the variable we are differentiating with respect to. We treat all other variables as constants and use the standard rules of differentiation, such as the power rule or product rule, to find the derivative.
Partial derivatives are important in many fields of science, including physics, economics, and engineering. They allow us to analyze how a function changes in response to small changes in its input variables, which can help us understand the behavior of complex systems and make predictions about their future behavior.
A partial derivative measures the change in a function with respect to one variable, while holding all other variables constant. A total derivative, on the other hand, measures the overall change in a function when all of its variables are allowed to vary. In other words, a total derivative takes into account the effects of all variables, while a partial derivative only considers one variable at a time.
Sure. Let's say we have a function f(x,y) = x2 + 2xy + y2. To find the partial derivative with respect to x, we treat y as a constant and use the power rule to get fx = 2x + 2y. Similarly, the partial derivative with respect to y would be fy = 2x + 2y. This tells us that the rate of change of f with respect to x is twice that of y, and that the rate of change is dependent on the values of both x and y.