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

Problem

d()/d(x)*(9√(,x)+8)*x^2

Solution

1. Distribute the x^2 term into the parentheses to simplify the expression before differentiating.

y=9*x^(1/2)⋅x^2+8*x^2

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

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

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

d(y)/d(x)=9⋅5/2*x^(3/2)+8⋅2*x^1

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)*x^2=45/2*x^(3/2)+16*x

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