Question:
\(\dfrac{d}{dx}\left(11^x\right)=\) ?
\(\dfrac{d}{dx}\left(11^x\right)=\) ?
Show Hint
Don't mix with power rule \(x^n\). Here the variable is in the exponent.
Updated On: Oct 17, 2025
- \(x\,11^{x-1}\)
- \(11^x\cdot \log x\)
- \(11^x\cdot \log 11\)
- \(\dfrac{11^x}{\log 11}\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
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 \(\dfrac{d}{dx}(11^x)=11^x\ln 11=11^x\cdot \log 11\).
So \(\dfrac{d}{dx}(11^x)=11^x\ln 11=11^x\cdot \log 11\).
Was this answer helpful?
0
0
Top Bihar Board XII Mathematics Questions
- \(\frac{d}{dx} \left(\sec^2 x - \tan^2 x\right)\)
- \(\frac{d}{dx} \left( e^{2x} + 2e^x \right)\)
- \(\frac{d}{dx} \left[ \lim_{x \to a} \frac{x^n + a^n}{x + a} \right] \)
- \(\frac{d}{dx} \left( \sin^{-1} 2x \right)\)
- \(\frac{d}{dx} \left[ (x+2)(x^2 - 2x + 4) \right] \)
View More Questions
Top Bihar Board XII Differentiation Questions
- \(\frac{d}{dx} \left[ (x+2)(x^2 - 2x + 4) \right] \)
- Find \( \frac{d}{dx} \left( \log 5x \right) \).
- Find \( \frac{d}{dx} \left(e^{3-2x}\right) \).
- Find the derivative of \[ \frac{d}{dx} \left\{ \left| x \right|^2 \right\}. \]
- Find the derivative: \[ \frac{d}{dx} \left[ \sin^{-1}\left( 2x \sqrt{1 - x^2} \right) \right] \]
View More Questions
Top Bihar Board XII Questions
- Which metal was first used by humans?
- Where is the Harappan site called Shortughai located?
- Where has the evidence of dockyard been found from Indus Valley Civilization?
- Which is referred to as Meluhha in Mesopotamian texts?
- Where have miniature pots of faience probably used as perfume bottles been found?
View More Questions