Question

find the derivative of ( f(x) ).

( f(x)=7 cdot 10^{x}+10 cdot 3^{x}-4 cdot 7^{x} )

( f^{prime}(x)= )

Explanation:

Step1: Use derivative rule for \(a^{x}\)

The derivative of \(a^{x}\) is \(a^{x}\ln a\).

Step2: Differentiate each term

For \(7\cdot10^{x}\), derivative is \(7\cdot10^{x}\ln10\).
For \(10\cdot3^{x}\), derivative is \(10\cdot3^{x}\ln3\).
For \(-4\cdot7^{x}\), derivative is \(-4\cdot7^{x}\ln7\).

Step3: Combine terms

\(f^{\prime}(x)=7\cdot10^{x}\ln10 + 10\cdot3^{x}\ln3-4\cdot7^{x}\ln7\)

Answer:

\(7\cdot10^{x}\ln10 + 10\cdot3^{x}\ln3-4\cdot7^{x}\ln7\)