Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems If y = x [ ( cos x 2 + sin x 2 ) ( cos x 2 − sin x 2 ) + sin x ] + 1 2 x y = x \left[ \left( \cos \frac{x}{2} + \sin \frac{x}{2} \right) \left( \cos \frac{x}{2} - \sin \frac{x}{2} \right) + \sin x \right] + \frac{1}{2\sqrt{x}} y = x [ ( cos 2 x + sin 2 x ) ( cos 2 x − sin 2 x ) + sin x ] + 2 x 1
Mathematics
Problem If y = x [ ( cos x 2 + sin x 2 ) ( cos x 2 − sin x 2 ) + sin x ] + 1 2 x y = x \left[ \left( \cos \frac{x}{2} + \sin \frac{x}{2} \right) \left( \cos \frac{x}{2} - \sin \frac{x}{2} \right) + \sin x \right] + \frac{1}{2\sqrt{x}} y = x [ ( cos 2 x + sin 2 x ) ( cos 2 x − sin 2 x ) + sin x ] + 2 x 1 d y d x = \frac{dy}{dx} = d x d y = ( 1 + x ) cos x + ( 1 − x ) sin x − 1 4 x x (1+x)\cos x + (1-x)\sin x - \frac{1}{4x\sqrt{x}} ( 1 + x ) cos x + ( 1 − x ) sin x − 4 x x 1 ( 1 − x ) cos x + ( 1 + x ) sin x + 1 4 x x (1-x)\cos x + (1+x)\sin x + \frac{1}{4x\sqrt{x}} ( 1 − x ) cos x + ( 1 + x ) sin x + 4 x x 1 ( 1 + x ) cos x + ( 1 + x ) sin x − 1 4 x x (1+x)\cos x + (1+x)\sin x - \frac{1}{4x\sqrt{x}} ( 1 + x ) cos x + ( 1 + x ) sin x − 4 x x 1 Browse the problem library