What is the derivative of 8arcsin(e^{x/2}) ?

The derivative of 8arcsin(e^{x/2}) is (4e^{x/2})/(sqrt(1-e^x))

What is the first derivative of 8arcsin(e^{x/2}) ?

The first derivative of 8arcsin(e^{x/2}) is (4e^{x/2})/(sqrt(1-e^x))

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derivative of

8 arcsin (e^{\frac{x}{2}})

\frac{4 e ^{\frac{x}{2}}}{1 - e ^{x}}

Solution steps

\frac{d}{d x} (8 arcsin (e^{\frac{x}{2}}))

Take the constant out:

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

= 8 \frac{d}{d x} (arcsin (e^{\frac{x}{2}}))

Apply the chain rule:

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

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

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

= 8 \cdot \frac{1}{1 - ( e ^{\frac{x}{2}} ) ^{2}} e^{\frac{x}{2}} \frac{1}{2}

Simplify

8 \cdot \frac{1}{1 - ( e ^{\frac{x}{2}} ) ^{2}} e^{\frac{x}{2}} \frac{1}{2} : \frac{4 e ^{\frac{x}{2}}}{1 - e ^{x}}

= \frac{4 e ^{\frac{x}{2}}}{1 - e ^{x}}

\frac{s}{s ^{2} ( s ^{2} + 1 )}

\frac{d}{d t} (e^{2 t})

(1 - x)^{- \frac{1}{2}}, 4

y = x^{2} - 3

f (x) = x sin (\frac{4}{x})

What is the derivative of 8arcsin(e^{x/2}) ?
The derivative of 8arcsin(e^{x/2}) is (4e^{x/2})/(sqrt(1-e^x))
What is the first derivative of 8arcsin(e^{x/2}) ?
The first derivative of 8arcsin(e^{x/2}) is (4e^{x/2})/(sqrt(1-e^x))