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

Problem

d()/d(x)*7

Solution

1. Identify the function as an exponential function of the form au where a=7 and u=√(,x)

2. Apply the chain rule for exponential functions, which states d(au)/d(x)=au⋅ln(a)⋅d(u)/d(x)

3. Differentiate the exponent u=√(,x)=x(1/2) using the power rule to get d(u)/d(x)=1/2*x(−1/2)=1/(2√(,x))

4. Substitute the components back into the chain rule formula.

5. Simplify the resulting expression into a single fraction.

Final Answer

d(7)/d(x)=(7*ln(7))/(2√(,x))

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