Solved: "Use the rules for derivatives to find the..."

erurnSopSoypegx

Answered question

2021-12-05

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

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

Answer & Explanation

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}{d x} (a^{g (x)}) = (\ln a) a^{g (x)} g^{'} (x)

Thus, here we will let

g (x) = \sqrt{x} \Rightarrow g^{'} (x) = \frac{1}{2 \sqrt{x}}

Step 4: Calculation
Hence, the required derivatives is as follows,

\frac{d y}{d x} = 10 \cdot \frac{d}{d x} (2^{\sqrt{x}})

= 10 (\ln 2) 2^{\sqrt{x}} (\frac{1}{2 \sqrt{x}})

= \frac{5}{\sqrt{x}} (\ln 2) 2^{\sqrt{x}}

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