You can differentiate a function when it only contains one changing variable, like f(x) = x2. It's derivative is f'(x) = 2x.
If a function contains more than one variable, like f(x,y) = x2 + y2, you can't just "find the derivative" generically because that doesn't specify what variable to take the derivative with respect to. Instead, you might "take the derivative with respect to x (treating y as a constant)" and get fx(x,y) = 2x or "take the derivative with respect to y (treating x as a constant)" and get fy(x,y) = 2y.
This is a partial derivative--when you take the derivative of a function with many variable with respect to one of the variables while treating the rest as constants.
in case of partial differentiation , suppose a z is a function of x and y so in partial differentiation of z w.r.t x all other variables except x are considered to be constant but on the contrary in differentiation process they are not considered as constant unless stated .
Suppose, Z is a function of X and Y. In case of Partial Differentiation of Z with respect to X, all other variables, except X are treated as constants. But, total derivative pf z is given by, dz=(partial derivative of z w.r.t x)dx + (partial derivative of z w.r.t y)dy
The difference between paraplegic, or paraplegia, and paraparesis is that parapelegia is a motor and sensory function impairment and paraparesis is partial paralysis.
The Exner equation describes conservation of mass between sediment in the bed of a channel and sediment that is being transported. It is expressed as partial differentiation of n with respect to t=-(1/epsilon0) x partial differentiation of q with respect to x.
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The lagrange function, commonly denoted L is the lagrangian of a system. Usually it is the kinetic energy - potential energy (in the case of a particle in a conservative potential). The lagrange equation is the equation that converts a given lagrangian into a system of equations of motion. It is d/dt(\partial L/\partial qdot)-\partial L/\partial q.
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Hugh Thurston has written: 'Differentiation and integration' 'Partial differentiation' -- subject(s): Calculus, Differential, Differential calculus
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Rate of diffusion increase with the difference of partial pressure of gas between different location. The partial pressure alone is not enough to define what the diffusion rate is, it require difference in concentration or partial pressure.
total differentiation is closer to implicit differentiation although you are not solving for dy/dx. in other words: the total derivative of f(x1,x2,...,xk) with respect to xn= [df(x1,x2,...,xk)/dx1][dx1/dxn] + df(x1,x2,...,xk)/dx2[dx2/dxn]+...+df(x1,x2,...,xk)/dxn +[df(x1,x2,...,xk)/dxn+1][dxn+1/dxn]+...+[df(x1,x2,...,xk)/dxk][dxk/dxn] however, the partial derivative is not this way. the partial derivative of f(x1,x2,...,xk) with respect to xn is just that, can't be expanded. The chain rule is not the same as total differentiation either. The chain rule is for partially differentiating f(x1,x2,...,xk) with respect to a variable not included in the explicit form. In other words, xn has to be considered a function of this variable for all integers n. so the total derivative is similar to the chain rule, but not the same.