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(x^n)/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))

Want more problems? Check here!