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Calculus 3: Partial derivatives

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Finding Partial Derivatives of a Function

Consider the function f(x,y) = xy^2 + x^3, and find the partial derivatives with respect to x and y.

Partial derivativesEasyVideo
Partial Derivatives of a Function of Two Variables

Compute the partial derivatives ∂f∂x\frac{\partial f}{\partial x} and ∂f∂y\frac{\partial f}{\partial y} for the function f(x,y)=x2⋅y+sin⁡(y)f(x, y) = x^2 \cdot y + \sin(y).

Partial derivativesEasyVideo
Partial Derivatives of a Temperature Distribution Function

If the temperature distribution over a flat slab of metal is described by a function of two variables, like f(x,y)=9−x2−y2f(x, y) = 9 - x^2 - y^2, what is the partial derivative of this function with respect to xx and yy?

Partial derivativesEasyVideo
Partial Derivative with Respect to X

Calculate the partial derivative of a function Z with respect to X, holding Y constant.

Partial derivativesEasyVideoNeeds Attention
Calculating Partial Derivative of Z with Respect to Y

Calculate the partial derivative of a function Z with respect to Y, holding X constant.

Partial derivativesEasyVideoNeeds Attention
Identifying Critical Points in Multivariable Function

Given a multivariable function f(x,y)=x2+y2f(x,y) = x^2 + y^2, find where the partial derivatives are equal to zero to identify candidates for maximums or minimums.

Partial derivativesEasyVideo