Differentiation Question 179
Question: If $ y=f( \frac{5x+1}{10x^{2}-3} ) $ and $ f’(x)=\cos x $ , then $ \frac{dy}{dx}= $
[MP PET 1987]
Options:
A) $ \cos ( \frac{5x+1}{10x^{2}-3} )\frac{dy}{dx}( \frac{5x+1}{10x^{2}-3} ) $
B) $ \frac{5x+1}{10x^{2}-3}\cos ( \frac{5x+1}{10x^{2}-3} ) $
C) $ \cos ( \frac{5x+1}{10x^{2}-3} ) $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Suppose that $ t=\frac{5x+1}{10x^{2}-3}, $ so $ y=f(t) $
$ \therefore \frac{dy}{dx}={f}’(t).\frac{dt}{dx} $
[Since $ f’(x)=\cos x $ ] $ \frac{dy}{dx}=\cos ( \frac{5x+1}{10x^{2}-3} )\frac{d}{dx}( \frac{5x+1}{10x^{2}-3} ). $
BETA
