Question

find the antiderivative for each function when c equals 0

a. ( f(x)=6^{x} ) b. ( g(x)=7^{-x} ) c. ( h(x)=left(\frac{7}{6}
ight)^{x} )

a. ( f(x)=square )

Explanation:

Step1: Recall the antiderivative formula for \(a^x\)

The antiderivative of \(a^x\) is \(\frac{a^x}{\ln a}+C\). For \(f(x) = 6^x\) and \(C = 0\).

Step2: Apply the formula

Substitute \(a = 6\) into the formula \(\frac{a^x}{\ln a}+C\). We get \(\frac{6^x}{\ln 6}+0\).

Answer:

\(\frac{6^x}{\ln 6}\)