What is the derivative of arcsin(e^x) ?

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

What is the first derivative of arcsin(e^x) ?

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

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derivative of

arcsin (e^{x})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

3^{x} + 2

lo g_{10} (\frac{2}{x})

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

t^{2} + 2 t + 4

(sin (x) + cos (x))^{3}

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