# Is there a chain rule for partial derivatives?

Yes, there is.

This is similar to the chain rule you see when doing related rates, for instance.

You may see that this is a convenient notation that allows you to see the rationale for formulating the way you take these partial derivatives:

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Yes, there is a chain rule for partial derivatives, often referred to as the multivariable chain rule. It states that if a function z = f(x, y) depends on variables x and y, where x and y are themselves functions of other variables u and v respectively, then the partial derivative of z with respect to u can be expressed as the sum of the partial derivatives of z with respect to x and y, multiplied by the corresponding partial derivatives of x and y with respect to u and v, respectively. Mathematically, it can be written as ∂z/∂u = (∂z/∂x)(∂x/∂u) + (∂z/∂y)(∂y/∂u).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you use the chain rule to differentiate #y=(4x^3-7)^4(3x+2)^10#?
- How do you differentiate #f(x)=sec(e^(x)-3x ) # using the chain rule?
- How do you find the derivative of #f(x)=1/4x^2-x+4#?
- How do you use implicit differentiation to find the slope of the curve given #xy^5+x^5y=1# at (-1,-1)?
- How do you differentiate # f(x)=e^sqrt(3x+x^2)# using the chain rule.?

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