Find the Derivative - d/dx y=(3 square root of x+2)x^2

Problem

d()/d(x)*(3√(,x)+2)*x^2

Solution

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

y=3*x^(1/2)⋅x^2+2*x^2

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

y=3*x^(5/2)+2*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)=3⋅5/2*x^(5/2−1)+2⋅2*x^(2−1)

4. Simplify the coefficients and the exponents to find the final derivative.

d(y)/d(x)=15/2*x^(3/2)+4*x

Final Answer

(d(3√(,x)+2)*x^2)/d(x)=15/2*x^(3/2)+4*x

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