Задача 11 (Похідна добутку)

Обчислити похідну функції  y=x\cdot 2^{\sqrt{x}} .

 y'=\left(x\cdot 2^{\sqrt{x}} \right)'=x'\cdot 2^{\sqrt{x}}+x\cdot \left(2^{\sqrt{x}} \right)'=

 =1\cdot 2^{\sqrt{x}}+x\cdot 2^{\sqrt{x}}\cdot ln2\cdot \left(\sqrt{x} \right)'=

 =2^{\sqrt{x}}+x\cdot 2^{\sqrt{x}}\cdot ln2\cdot \frac{1}{2\sqrt{x}}=

 =2^{\sqrt{x}}+\frac{x\cdot ln2\cdot 2^{\sqrt{x}-1}}{\sqrt{x}}=2^{\sqrt{x}}+ln2\cdot \sqrt{x}\cdot 2^{\sqrt{x}-1}

2 Responses to “Задача 11 (Похідна добутку)”

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