Find the Derivative - d/dx y=(9 square root of x+8)x^2

Problem

d()/d(x)*(9√(,x)+8)*x2

Solution

1. Distribute the x2 term into the parentheses to simplify the expression before differentiating.

y=9*x(1/2)⋅x2+8*x2

2. Simplify the exponents using the rule xa⋅xb=x(a+b) where 1/2 + 2 = 5/2$.

y=9*x(5/2)+8*x2

3. Apply the power rule, which states d(xn)/d(x)=n*x(n−1) to each term individually.

d(y)/d(x)=9⋅5/2*x(3/2)+8⋅2*x1

4. Multiply the constants to find the final derivative.

d(y)/d(x)=45/2*x(3/2)+16*x

Final Answer

d()/d(x)*(9√(,x)+8)*x2=45/2*x(3/2)+16*x

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