Find the first and second partial derivatives of the function f(x, y) = (8 + 7xy)e^(-5x^2-8y^2) f_x = (7y)(e^(-5x^2-8y^2)) + ((8+7xy)(e^(-5x^2-8y^2))(-10x)) f_y = (7x)(e^(-5x^2-8y^2)) + ((8+7xy)(e^(-5x^2-8y^2))(-16y)) f_xx = (7y)(e^(-5x^2-8y^2))(-10x) + (7x)(10x)(e^(-5x^2-8y^2)) + (8+7xy)(e^(-5x^2-8y^2))(-10x)^2 f_yy = (7y)(e^(-5x^2-8y^2))(-16y) + (7x)(e^(-5x^2-8y^2)) + (8+7xy)(e^(-5x^2-8y^2))(-16y)^2
Added by Emilia L.
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Step 1: To find the first partial derivative with respect to x, we use the product rule and the chain rule. Show more…
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