What is the derivative of e^{-0.5}(2x+1)^{0.5} ?

The derivative of e^{-0.5}(2x+1)^{0.5} is (0.60653…)/((2x+1)^{1/2)}

What is the first derivative of e^{-0.5}(2x+1)^{0.5} ?

The first derivative of e^{-0.5}(2x+1)^{0.5} is (0.60653…)/((2x+1)^{1/2)}

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derivative of

e^{- 0.5} (2 x + 1)^{0.5}

\frac{0.60653 \dots}{( 2 x + 1 ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (e^{- 0.5} (2 x + 1)^{0.5})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= e^{- 0.5} \frac{d}{d x} ((2 x + 1)^{0.5})

Apply the chain rule:

\frac{0.5}{( 2 x + 1 ) ^{0.5}} \frac{d}{d x} (2 x + 1)

= \frac{0.5}{( 2 x + 1 ) ^{0.5}} \frac{d}{d x} (2 x + 1)

\frac{d}{d x} (2 x + 1) = 2

= e^{- 0.5} \frac{0.5}{( 2 x + 1 ) ^{0.5}} \cdot 2

Simplify

e^{- 0.5} \frac{0.5}{( 2 x + 1 ) ^{\frac{1}{2}}} \cdot 2 : \frac{0.60653 \dots}{( 2 x + 1 ) ^{\frac{1}{2}}}

= \frac{0.60653 \dots}{( 2 x + 1 ) ^{\frac{1}{2}}}

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What is the derivative of e^{-0.5}(2x+1)^{0.5} ?
The derivative of e^{-0.5}(2x+1)^{0.5} is (0.60653…)/((2x+1)^{1/2)}
What is the first derivative of e^{-0.5}(2x+1)^{0.5} ?
The first derivative of e^{-0.5}(2x+1)^{0.5} is (0.60653…)/((2x+1)^{1/2)}