A) \[\frac{1}{27}{{x}^{2}}{{(2{{x}^{3}}+15)}^{3}}\]
B) \[\frac{2}{27}x{{(2{{x}^{3}}+5)}^{3}}\]
C) \[\frac{2}{27}{{x}^{2}}{{(2{{x}^{3}}+15)}^{3}}\]
D) None of these
Correct Answer: C
Solution :
\[\frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx}={{u}^{3}}.2{{x}^{2}}\] \[={{\left( \frac{2}{3}{{x}^{3}}+5 \right)}^{3}}.2{{x}^{2}}=\frac{2}{27}{{x}^{2}}{{(2{{x}^{3}}+15)}^{3}}\].
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