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2021-12-05

Use the rules for derivatives to find the derivative of function defined as follows.

$y=10\cdot {2}^{\sqrt{x}}$

Gloria Lusk

Beginner2021-12-06Added 18 answers

Step 1: Consider the given

Function,$y=10\cdot {2}^{\sqrt{x}}$

Step 2: The objective

Is to find the derivative of the function.

Step 3: Concept used

Since, we know,$\frac{d}{dx}\left({a}^{g\left(x\right)}\right)=\left(\mathrm{ln}a\right){a}^{g\left(x\right)}{g}^{\prime}\left(x\right)$

Thus, here we will let$g\left(x\right)=\sqrt{x}\Rightarrow {g}^{\prime}\left(x\right)=\frac{1}{2\sqrt{x}}$

Step 4: Calculation

Hence, the required derivatives is as follows,

$\frac{dy}{dx}=10\cdot \frac{d}{dx}\left({2}^{\sqrt{x}}\right)$

$=10\left(\mathrm{ln}2\right){2}^{\sqrt{x}}\left(\frac{1}{2\sqrt{x}}\right)$

$=\frac{5}{\sqrt{x}}\left(\mathrm{ln}2\right){2}^{\sqrt{x}}$

Function,

Step 2: The objective

Is to find the derivative of the function.

Step 3: Concept used

Since, we know,

Thus, here we will let

Step 4: Calculation

Hence, the required derivatives is as follows,