Find the Derivative - d/dx e^(7 square root of x)

Problem

d(e(7√(,x)))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule, where the outer function is eu and the inner function is u=7√(,x)

2. Differentiate the outer function with respect to u which results in eu

3. Rewrite the inner function 7√(,x) as 7*x(1/2) to prepare for the Power Rule.

4. Differentiate the inner function using the Power Rule: (d(7)*x(1/2))/d(x)=7⋅1/2*x(−1/2)

5. Simplify the derivative of the inner function to 7/(2√(,x))

6. Combine the results using the Chain Rule formula d(y)/d(x)=d(y)/d(u)⋅d(u)/d(x)

Final Answer

d(e(7√(,x)))/d(x)=(7*e(7√(,x)))/(2√(,x))

Want more problems? Check here!