Find dy/dx y=e^(7 square root of x)

Problem

d()/d(x)*e^(7√(,x))

Solution

1. Identify the outer and inner functions to apply the chain rule for the expression y=e^u where u=7√(,x)

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

3. Differentiate the inner function u=7*x^(1/2) with respect to x using the power rule.

d(u)/d(x)=7⋅1/2*x^(−1/2)

4. Simplify the derivative of the inner function.

d(u)/d(x)=7/(2√(,x))

5. Combine the results using the chain rule d(y)/d(x)=d(y)/d(u)⋅d(u)/d(x)

d(y)/d(x)=e^(7√(,x))⋅7/(2√(,x))

Final Answer

d(y)/d(x)=(7*e^(7√(,x)))/(2√(,x))

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