Find dy/dx y=e^(9 square root of x)

Problem

d()/d(x)*e(9√(,x))

Solution

1. Identify the outer and inner functions to apply the chain rule for the expression y=eu where u=9√(,x)

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

3. Differentiate the inner function u=9*x(1/2) with respect to x using the power rule.

d(u)/d(x)=9⋅1/2*x(−1/2)

4. Simplify the derivative of the inner function.

d(u)/d(x)=9/(2√(,x))

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

d(y)/d(x)=e(9√(,x))⋅9/(2√(,x))

6. Rearrange the terms into a single fraction.

d(y)/d(x)=(9*e(9√(,x)))/(2√(,x))

Final Answer

d(y)/d(x)=(9*e(9√(,x)))/(2√(,x))

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