Question

\(\dfrac{d}{dx}\left(11^x\right)=\) ?

• A. \(x\,11^{x-1}\)
• B. \(11^x\cdot \log x\)
• C. \(11^x\cdot \log 11\)
• D. \(\dfrac{11^x}{\log 11}\)

Hint:

Don't mix with power rule \(x^n\). Here the variable is in the exponent.

Answer 1

The Correct Option is C

Idea. For base \(a\) (constant), \(\dfrac{d}{dx}(a^x)=a^x\ln a\). \(\ln\) and \(\log\) (base \(e\)) are the same in calculus notation here.
So \(\dfrac{d}{dx}(11^x)=11^x\ln 11=11^x\cdot \log 11\).