Mathematic Problems

Mathematic Problems

150. példa

Bárczy Barnabás: Differential Calculus - 5. )

y = \sqrt{x} \cdot \sin x

y = x^{\frac{1}{2}} \cdot \sin x

u = x^{\frac{1}{2}}; v = s i n x \Rightarrow y = u \cdot v

u' = \frac{1}{2} x^{\frac{1}{2} - 1} = \frac{1}{2} x^{- \frac{1}{2}}; v' = \cos x

y' = u' \cdot v + u \cdot v'

y' = \frac{1}{2} x^{- \frac{1}{2}} \cdot s i n x + x^{\frac{1}{2}} \cdot c o s x

y' = \frac{\sin x}{2 \sqrt{x}} + \sqrt{x} \cdot \cos x

y' = \frac{\sin x}{2 \sqrt{x}} + \sqrt{x} \cdot \cos x