Find the 2nd Derivative f(x) = square root of x

Problem

ƒ(x)=√(,x)

Solution

1. Rewrite the function using a fractional exponent to make it easier to differentiate.

ƒ(x)=x(1/2)

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

ƒ(x)′=1/2*x(−1/2)

3. Apply the power rule again to the first derivative to find the second derivative.

ƒ(x)″=1/2⋅(−1/2)*x(−3/2)

4. Simplify the coefficients and rewrite the expression with a positive exponent in the denominator.

ƒ(x)″=−1/4*x(−3/2)

ƒ(x)″=−1/(4*x(3/2))

Final Answer

d2(√(,x))/(d(x)2)=−1/(4*x√(,x))

Want more problems? Check here!