Find the 2nd Derivative f(x)=7x^(3/2)

Problem

ƒ(x)=7*x(3/2)

Solution

1. Identify the function and the goal, which is to find the second derivative ƒ(x)″ by differentiating twice with respect to x

2. Apply the power rule to find the first derivative ƒ(x)′ The power rule states d(xn)/d(x)=n*x(n−1)

ƒ(x)′=7⋅3/2*x(3/2−1)

3. Simplify the expression for the first derivative.

ƒ(x)′=21/2*x(1/2)

4. Apply the power rule again to the first derivative to find the second derivative ƒ(x)″

ƒ(x)″=21/2⋅1/2*x(1/2−1)

5. Simplify the final expression by multiplying the constants and subtracting the exponents.

ƒ(x)″=21/4*x(−1/2)

Final Answer

ƒ(x)″=21/(4√(,x))

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