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# partial derivative watch

1. Hello guys! I'm currently stuck in two problems regarding partial differentiation: I don't know which formula or formulas to use and how to use them, so please help!

1) Find the partial derivative ∂m/∂q and ∂m/∂h of/for the function:

m=ln(qh-2h^2)+2e^(q-h^2+3)^4-7

2) Find the partial derivative ∂z/∂x of/for the function:

(z+1)^3y-(zx)^2-3=x/z-ln(xyz)-5xy^2
2. (Original post by Lillery)
Hello guys! I'm currently stuck in two problems regarding partial differentiation: I don't know which formula or formulas to use and how to use them, so please help!

1) Find the partial derivative ∂m/∂q and ∂m/∂h of/for the function:

m=ln(qh-2h^2)+2e^(q-h^2+3)^4-7

2) Find the partial derivative ∂z/∂x of/for the function:

(z+1)^3y-(zx)^2-3=x/z-ln(xyz)-5xy^2
There aren't any "special formulas" to use - you are simply using the normal rules of differentiation (product rule and chain rule principally) - but you just have to keep in mind which are your dependent and independent variables, and with respect to which variable you are differentiating - the others can be treated as constants.

So for 1), m is a function of q and h. When you differentiate with respect to q, you treat h as a constant. and vice versa.

2) looks like the variable z is being treated as a function of x and y, and all 3 variables are related implicitly by the equation you are given. So differentiate both sides of that equation with respect to x, treating y as a constant (independent of x) - you will get terms on both sides that involve partial dz by partial dx, so you will need to rearrange the end result to isolate the derivate.

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Updated: October 25, 2015
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