What is the derivative of 4arcsin(e^{x/2}) ?

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

What is the first derivative of 4arcsin(e^{x/2}) ?

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

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derivative of

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

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

Solution steps

\frac{d}{d x} (4 arcsin (e^{\frac{x}{2}}))

Take the constant out:

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

= 4 \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}

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

Simplify

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

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

\frac{d}{d x} (y x^{2})

\frac{\partial}{\partial x} (sin (- x) cos (2 y))

x \to 0 lim (\frac{ln ( 3 x + 1 )}{x})

19 - x^{2}

\frac{\partial}{\partial x} (ln (x^{2} + y^{2}))

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