Mathematic Problems

249. példa

y = \ln \sin^{2} x

y = \ln \sin^{2} x

g = s i n^{2} x \Rightarrow y = \ln g

u = s i n x; u' = c o s x \Rightarrow g = u^{2} \Rightarrow g' = 2 \cdot u \cdot u' = 2 \cdot s i n x \cdot c o s x

y' = \frac{1}{g} \cdot g'

y' = \frac{1}{\sin^{2} x} \cdot 2 \cdot s i n x \cdot \cos x

y' = \frac{2 \cos x}{\sin x}

y' = 2 c t g x

y' = 2 c t g x

Matematika - Képlettár