Differentiation Question 13
Question: If $ y=\frac{1}{4}u^{4},u=\frac{2}{3}x^{3}+5 $ , then $ \frac{dy}{dx}= $
[DSSE 1979]
Options:
A) $ \frac{1}{27}x^{2}{{(2x^{3}+15)}^{3}} $
B) $ \frac{2}{27}x{{(2x^{3}+5)}^{3}} $
C) $ \frac{2}{27}x^{2}{{(2x^{3}+15)}^{3}} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx}=u^{3}.2x^{2} $
$ ={{( \frac{2}{3}x^{3}+5 )}^{3}}.2x^{2}=\frac{2}{27}x^{2}{{(2x^{3}+15)}^{3}} $ .
BETA
