Find the Derivative - d/dx 5^(7x)

Problem

d(5^(7*x))/d(x)

Solution

1. Identify the rule for differentiating an exponential function of the form a^u where a is a constant and u is a function of x

2. Apply the formula for the derivative of a^u which is d(a^u)/d(x)=a^u⋅ln(a)⋅d(u)/d(x)

3. Substitute a=5 and u=7*x into the formula.

4. Differentiate the exponent u=7*x with respect to x which gives (d(7)*x)/d(x)=7

5. Simplify the expression by combining the constants.

Final Answer

d(5^(7*x))/d(x)=7⋅5^(7*x)*ln(5)

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