Find the 2nd Derivative 10x^9y^5+7x^4y^8

Problem

d2()/(d(x)2)*(10*x9*y5+7*x4*y8)

Solution

1. Identify the expression as a function of x and y and determine that the task is to find the second partial derivative with respect to x denoted as (ƒ_x*x) or ∂2(ƒ)/(∂(x)2)

2. Find the first derivative with respect to x by treating y as a constant and applying the power rule to the x terms.

d()/d(x)*(10*x9*y5+7*x4*y8)=90*x8*y5+28*x3*y8

3. Find the second derivative by differentiating the first derivative with respect to x once more, again treating y as a constant.

d()/d(x)*(90*x8*y5+28*x3*y8)=720*x7*y5+84*x2*y8

Final Answer

d2()/(d(x)2)*(10*x9*y5+7*x4*y8)=720*x7*y5+84*x2*y8

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