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How to take derivative of two variables?
To take the derivative of a function with two variables, you can use partial derivatives. For a function ( f(x, y) ), the partial derivative with respect to ( x ) is denoted as ( \frac{\partial f}{\partial x} ) and is calculated by treating ( y ) as a constant. Similarly, the partial derivative with respect to ( y ) is denoted as ( \frac{\partial f}{\partial y} ) and is found by treating ( x ) as a constant. You can compute these derivatives using standard differentiation rules applied to each variable individually.
Since there is something called a partial derivative in calculus is there a partial integral?
Certainly. It uses the same symbol as the full integral, but you still treat the other independent variables as constants.
What is the derivative of root sin2x?
You are supposed to use the chain rule for this. First step: derivative of root of sin2x is (1 / (2 root of sin 2x)) times the derivative of sin 2x. Second step: derivative of sin 2x is cos 2x times the derivative of 2x. Third step: derivative of 2x is 2. Finally, you need to multiply all the parts together.
What is the 87th derivative of sin x?
Every fourth derivative, you get back to "sin x" - in other words, the 84th derivative of "sin x" is also "sin x". From there, you need to take the derivative 3 more times, getting:85th derivative: cos x86th derivative: -sin x87th derivative: -cos x
What is the derivative with respect to x of 20xy?
This is technically a partial derivative, represented as ∂(20xy)/∂x. The way to calculate this is simple, treat y as a constant, like 20 is in this case. Therefore, the expression is simplified to 20*y*d(x)/dx. d(x)/dx is just 1, so the answer is 20y.
What is the difference between total differentiation and partial differentiation?
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
What is a partial derivative?
A partial derivative is the derivative of a function of more than one variable with respect to only one variable. When taking a partial derivative, the other variables are treated as constants. For example, the partial derivative of the function f(x,y)=2x2 + 3xy + y2 with respect to x is:?f/?x = 4x + 3yhere we can see that y terms have been treated as constants when differentiating.The partial derivative of f(x,y) with respect to y is:?f/?y = 3x + 2yand here, x terms have been treated as constants.
What are spacial derivatives?
The spacial derivative is the measure of a quantity as and how it is being changed in space. This is different from a temporal derivative and partial derivative.
What are the applications of partial derivatives in real analysis?
what are the applications of partial derivative in real analysis.
What is the derivative of a function with respect to a vector?
The derivative of a function with respect to a vector is a matrix of partial derivatives.
What is the difference between partial derivative and derivative?
Say you have a function of a single variable, f(x). Then there is no ambiguity about what you are taking the derivative with respect to (it is always with respect to x). But what if I have a function of a few variables, f(x,y,z)? Now, I can take the derivative with respect to x, y, or z. These are "partial" derivatives, because we are only interested in how the function varies w.r.t. a single variable, assuming that the other variables are independent and "frozen". e.g., Question: how does f vary with respect to y? Answer: (partial f/partial y) Now, what if our function again depends on a few variables, but these variables themselves depend on time: x(t), y(t), z(t) --> f(x(t),y(t),z(t))? Again, we might ask how f varies w.r.t. one of the variables x,y,z, in which case we would use partial derivatives. If we ask how f varies with respect to t, we would do the following: df/dt = (partial f/partial x)*dx/dt + (partial f/partial y)*dy/dt + (partial f/partial z)*dz/dt df/dt is known as the "total" derivative, which essentially uses the chain rule to drop the assumption that the other variables are "frozen" while taking the derivative. This framework is especially useful in physical problems where I might want to consider spatial variations of a function (partial derivatives), as well as the total variation in time (total derivative).
What is the partial derivative of the van der Waals equation with respect to volume?
The partial derivative of the van der Waals equation with respect to volume is the derivative of the equation with respect to volume while keeping other variables constant.
How do you calculate uncertainty for a derivative?
To calculate uncertainty for a derivative, you must first identify the uncertainties in the variables involved in the function. Use the formula for propagation of uncertainty, which states that the uncertainty in the derivative ( \frac{dy}{dx} ) can be estimated as ( \sigma_{\frac{dy}{dx}} = \left| \frac{dy}{dx} \right| \sqrt{ \left( \frac{\partial y}{\partial x} \sigma_x \right)^2 + \left( \frac{\partial y}{\partial z} \sigma_z \right)^2 + \ldots } ), where ( \sigma_x ), ( \sigma_z ), etc., are the uncertainties in the respective variables. This approach allows you to obtain the total uncertainty associated with the derivative based on the uncertainties of the input variables.
What is the derivative of x-y?
The partial derivative in relation to x: dz/dx=-y The partial derivative in relation to y: dz/dy= x If its a equation where a constant 'c' is set equal to the equation c = x - y, the derivative is 0 = 1 - dy/dx, so dy/dx = 1
What is the derivative with respect to vector of the given function?
The derivative with respect to a vector of a function is a vector of partial derivatives of the function with respect to each component of the vector.
Is the marginal cost the derivative of the total cost?
Yes, the marginal cost is the derivative of the total cost.
What is the answer when partial derivative the strain?
The partial derivative of strain with respect to a specific variable, such as time or a spatial coordinate, quantifies how strain changes in relation to that variable while keeping other variables constant. In continuum mechanics, this can provide insights into the material's response to stress or deformation over time or space. For example, the partial derivative of strain with respect to time can indicate the rate of strain development in a material under loading conditions.
