What is the derivative of 10arcsin(e^{x/2}) ?

The derivative of 10arcsin(e^{x/2}) is (5e^{x/2})/(sqrt(1-e^x))

What is the first derivative of 10arcsin(e^{x/2}) ?

The first derivative of 10arcsin(e^{x/2}) is (5e^{x/2})/(sqrt(1-e^x))

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derivative of

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

\frac{5 e ^{\frac{x}{2}}}{1 - e ^{x}}

Solution steps

\frac{d}{d x} (10 arcsin (e^{\frac{x}{2}}))

Take the constant out:

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

= 10 \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}

= 10 \cdot \frac{1}{1 - ( e ^{\frac{x}{2}} ) ^{2}} e^{\frac{x}{2}} \frac{1}{2}

Simplify

10 \cdot \frac{1}{1 - ( e ^{\frac{x}{2}} ) ^{2}} e^{\frac{x}{2}} \frac{1}{2} : \frac{5 e ^{\frac{x}{2}}}{1 - e ^{x}}

= \frac{5 e ^{\frac{x}{2}}}{1 - e ^{x}}

\int \frac{4 x ^{2}}{x ^{2} + 7} d x

x \to 3 lim (\frac{1}{x - 2})

y^{^{''}} - y = \frac{e ^{x}}{1 + x ^{2}}

\frac{d}{d x} (lo g_{e} (7 x^{- 2}))

\frac{d}{d x} (\frac{x}{x ^{2} + 5})

What is the derivative of 10arcsin(e^{x/2}) ?
The derivative of 10arcsin(e^{x/2}) is (5e^{x/2})/(sqrt(1-e^x))
What is the first derivative of 10arcsin(e^{x/2}) ?
The first derivative of 10arcsin(e^{x/2}) is (5e^{x/2})/(sqrt(1-e^x))