Mathematic Problems

226. példa

y = \cos^{- 4} \sqrt{2 x}

y = \cos^{- 4} \sqrt{2 x}

= {[\cos {(2 x)}^{\frac{1}{2}}]}^{- 4}

y' = - 4 {[\cos {(2 x)}^{\frac{1}{2}}]}^{- 5} [- \sin {(2 x)}^{\frac{1}{2}}] \cdot \frac{1}{2} {(2 x)}^{- \frac{1}{2}} \cdot 2

= \frac{4 \sin \sqrt{2 x}}{\sqrt{2 x} {[\cos \sqrt{2 x}]}^{5}}

y' = \frac{4 \sin \sqrt{2 x}}{\sqrt{2 x} {[\cos \sqrt{2 x}]}^{5}}

Matematika - Képlettár