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Problem If y = f ( 5 x + 1 10 x 2 − 3 ) y = f \left( \frac{5x+1}{10x^2-3} \right) y = f ( 10 x 2 − 3 5 x + 1 ) f ′ ( x ) = cos x f'(x) = \cos x f ′ ( x ) = cos x d y d x = \frac{dy}{dx} = d x d y = cos ( 5 x + 1 10 x 2 − 3 ) d d x ( 5 x + 1 10 x 2 − 3 ) \cos \left( \frac{5x+1}{10x^2-3} \right) \frac{d}{dx} \left( \frac{5x+1}{10x^2-3} \right) cos ( 10 x 2 − 3 5 x + 1 ) d x d ( 10 x 2 − 3 5 x + 1 ) 5 x + 1 10 x 2 − 3 cos ( 5 x + 1 10 x 2 − 3 ) \frac{5x+1}{10x^2-3} \cos \left( \frac{5x+1}{10x^2-3} \right) 10 x 2 − 3 5 x + 1 cos ( 10 x 2 − 3 5 x + 1 ) cos ( 5 x + 1 10 x 2 − 3 ) \cos \left( \frac{5x+1}{10x^2-3} \right) cos ( 10 x 2 − 3 5 x + 1 ) Browse the problem library