Задача 8 (Похідна складеної функції)

Обчислити похідну функції  y=e^{arctg\sqrt{1+ln\left(2x+3 \right)}} .

♦  y'=e^{arctg\sqrt{1+ln\left(2x+3 \right)}}\cdot \frac{1}{1+\sqrt{1+ln\left(2x+3 \right)}^{2}}\times

  \times \frac{1}{2\sqrt{1+ln\left(2x+3 \right)}}\cdot \frac{1}{2x+3}\cdot 2=

  =\frac{e^{arctg\sqrt{1+ln\left(2x+3 \right)}}}{\left(2x+3 \right)\sqrt{1+ln\left(2x+3 \right)}\cdot \left(2+ln\left(2x+3 \right) \right)} .♦

3 Responses to “Задача 8 (Похідна складеної функції)”

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