What is the derivative of 6arcsin(e^{x/2}) ?

The derivative of 6arcsin(e^{x/2}) is (3e^{x/2})/(sqrt(1-e^x))

What is the first derivative of 6arcsin(e^{x/2}) ?

The first derivative of 6arcsin(e^{x/2}) is (3e^{x/2})/(sqrt(1-e^x))

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derivative of

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

\frac{3 e ^{\frac{x}{2}}}{1 - e ^{x}}

Solution steps

\frac{d}{d x} (6 arcsin (e^{\frac{x}{2}}))

Take the constant out:

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

= 6 \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}

= 6 \cdot \frac{1}{1 - ( e ^{\frac{x}{2}} ) ^{2}} e^{\frac{x}{2}} \frac{1}{2}

Simplify

6 \cdot \frac{1}{1 - ( e ^{\frac{x}{2}} ) ^{2}} e^{\frac{x}{2}} \frac{1}{2} : \frac{3 e ^{\frac{x}{2}}}{1 - e ^{x}}

= \frac{3 e ^{\frac{x}{2}}}{1 - e ^{x}}

\frac{d}{d x} (\frac{3 ^{x} + 8}{3 ^{x} - 1})

\int e^{- 0.25 x} d x

\int 2 x y^{2} d x

\frac{tan ( \frac{x}{2} ) + cot ( \frac{x}{2} )}{x}

3 cos^{2} (t)

What is the derivative of 6arcsin(e^{x/2}) ?
The derivative of 6arcsin(e^{x/2}) is (3e^{x/2})/(sqrt(1-e^x))
What is the first derivative of 6arcsin(e^{x/2}) ?
The first derivative of 6arcsin(e^{x/2}) is (3e^{x/2})/(sqrt(1-e^x))