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

Problem

d()/d(x)*7^√(,x)

Solution

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

2. Apply the chain rule for exponential functions, which states d(a^u)/d(x)=a^u⋅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^√(,x))/d(x)=(7^√(,x)*ln(7))/(2√(,x))

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