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Math Help - Some partial derivatives

  1. #1
    Junior Member
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    Some partial derivatives

    I've been asked to find the partial derivative with respect to x for the function:

    <br />
f(x,y) = 2xe^{x+y^2} - e^y + sinh(2x + y)<br />

    I've learnt about treating y as though it's a constant, and this is what I've got so far. However, I think my working is wrong or my rules haven't been applied correctly. My logic was to apply the product rule to the first grouping, treat e^y just as a constant and just differentiate the last grouping based on the rules for sinh. Here's the result I got:

    <br />
f_x(x,y) = 2x({e^{x+y^2}}\cdot{1}) + {e^{x+y^2}}\cdot{2} - 0 + {cosh(2x + y)}\cdot{2}<br />

    <br />
f_x(x,y) = 2e^{x+y^2}(x + 1) + 2cosh(2x+y)<br />

    Hopefully someone can shed some light on whether the working/answer is correct? I'm not feeling very confident about it.
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  2. #2
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    I think you got it right
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  3. #3
    Junior Member
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    Same problem with respect to y

    What about if I was to take the partial derivative with respect to y? Would it be:

    <br />
f_y(x,y) = 2x({e^{x+y^2}}\cdot{2y}) + {{e^{x + y^2}}\cdot{0}} - e^y + {cosh(2x + y)} \cdot {1}<br />

    <br />
f_y(x,y) = 4xye^{x+y^2} - e^y + cosh(2x + y)<br />
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  4. #4
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    Looks right
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