Differentiation Question 92
Question: If $ y={3^{x^{2}}} $ , then $ \frac{dy}{dx} $ is equal to
Options:
A) $ (x^{2}){3^{x^{2}-1}} $
B) $ 3x^{2}.2x $
C) $ {3^{x^{2}}}.2x.\log 3 $
D) $ (x^{2}-1).3 $
Show Answer
Answer:
Correct Answer: C
Solution:
Given $ y={3^{x^{2}}} $
$ \because \frac{d}{dx}(a^{x})=a^{x}{\log _{e}}a $
$ \therefore \frac{dy}{dx}={3^{x^{2}}}{\log _{e}}3\frac{d}{dx}(x^{2}) $
Therefore $ \frac{dy}{dx}={3^{x^{2}}}.2x.{\log _{e}}3 $ .
BETA
