What is the derivative of ((sqrt(2x+1)/(e+1))^e) ?

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

What is the first derivative of ((sqrt(2x+1)/(e+1))^e) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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