What is the derivative of 2^{arcsech(x}) ?

The derivative of 2^{arcsech(x}) is -(ln(2)*2^{arcsech(x)})/(xsqrt(x+1)\sqrt{-x+1)}

What is the first derivative of 2^{arcsech(x}) ?

The first derivative of 2^{arcsech(x}) is -(ln(2)*2^{arcsech(x)})/(xsqrt(x+1)\sqrt{-x+1)}

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

- \frac{ln ( 2 ) \cdot 2 ^{arcsech (x)}}{x x + 1 - x + 1}

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

2^{arcsech (x)} = e^{arcsech (x) l n (2)}

= \frac{d}{d x} (e^{arcsech (x) l n (2)})

Apply the chain rule:

e^{arcsech (x) l n (2)} \frac{d}{d x} (arcsech (x) ln (2))

= e^{arcsech (x) l n (2)} \frac{d}{d x} (arcsech (x) ln (2))

\frac{d}{d x} (arcsech (x) ln (2)) = - \frac{ln ( 2 )}{x x + 1 - x + 1}

= e^{arcsech (x) l n (2)} (- \frac{ln ( 2 )}{x x + 1 - x + 1})

Simplify

e^{arcsech (x) l n (2)} (- \frac{ln ( 2 )}{x x + 1 - x + 1}) : - \frac{ln ( 2 ) \cdot 2 ^{arcsech (x)}}{x x + 1 - x + 1}

= - \frac{ln ( 2 ) \cdot 2 ^{arcsech (x)}}{x x + 1 - x + 1}

\int \frac{x}{x ^{4} + 3} d x

\frac{12 s + 8}{( s - 1 ) ^{5}}

\frac{3}{x ^{3}} - \frac{1}{x ^{4}}

(26 \frac{2}{3}, 9), (5, 2.5)

x \to 0 lim (x^{2} cos (x))

What is the derivative of 2^{arcsech(x}) ?
The derivative of 2^{arcsech(x}) is -(ln(2)*2^{arcsech(x)})/(xsqrt(x+1)\sqrt{-x+1)}
What is the first derivative of 2^{arcsech(x}) ?
The first derivative of 2^{arcsech(x}) is -(ln(2)*2^{arcsech(x)})/(xsqrt(x+1)\sqrt{-x+1)}