What is the derivative of 12arcsin(e^{x/2}) ?

The derivative of 12arcsin(e^{x/2}) is (6e^{x/2})/(sqrt(1-e^x))

What is the first derivative of 12arcsin(e^{x/2}) ?

The first derivative of 12arcsin(e^{x/2}) is (6e^{x/2})/(sqrt(1-e^x))

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derivative of

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

\frac{6 e ^{\frac{x}{2}}}{1 - e ^{x}}

Solution steps

\frac{d}{d x} (12 arcsin (e^{\frac{x}{2}}))

Take the constant out:

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

= 12 \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}

= 12 \cdot \frac{1}{1 - ( e ^{\frac{x}{2}} ) ^{2}} e^{\frac{x}{2}} \frac{1}{2}

Simplify

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

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

\frac{7 x}{8}

\frac{d y}{d x} + 5 y = 0, y (0) = 2

f (x) = x^{3} - 4 x + 6, at x = 2

\int \frac{x ^{2} + 1}{( x - 3 ) ( x - 2 ) ^{2}} d x

f (x) = (- x^{2} + 9)^{2}

What is the derivative of 12arcsin(e^{x/2}) ?
The derivative of 12arcsin(e^{x/2}) is (6e^{x/2})/(sqrt(1-e^x))
What is the first derivative of 12arcsin(e^{x/2}) ?
The first derivative of 12arcsin(e^{x/2}) is (6e^{x/2})/(sqrt(1-e^x))