Find the 4th Derivative y=10x^3+9x^2

Problem

d4()/(d(x)4)*(10*x3+9*x2)

Solution

1. Find the first derivative by applying the power rule, which states d(xn)/d(x)=n*x(n−1)

d(y)/d(x)=30*x2+18*x

2. Find the second derivative by differentiating the first derivative with respect to x

d2(y)/(d(x)2)=60*x+18

3. Find the third derivative by differentiating the second derivative.

d3(y)/(d(x)3)=60

4. Find the fourth derivative by differentiating the constant result from the previous step. The derivative of any constant is 0

d4(y)/(d(x)4)=0

Final Answer

d4()/(d(x)4)*(10*x3+9*x2)=0

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