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Popular >

derivative of arcsin(2^x)

Solution

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

Solution

\frac{ln ( 2 ) \cdot 2 ^{x}}{1 - 4 ^{x}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2^{x}) = 2^{x} ln (2)

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

Simplify

\frac{1}{1 - ( 2 ^{x} ) ^{2}} \cdot 2^{x} ln (2) : \frac{ln ( 2 ) \cdot 2 ^{x}}{1 - 4 ^{x}}

= \frac{ln ( 2 ) \cdot 2 ^{x}}{1 - 4 ^{x}}

Popular Examples

y^{''}-4y^'+4y=1

y^{^{''}} - 4 y^{^{'}} + 4 y = 1

integral from 0 to infinity of e^{-st}

\int_{0}^{\infty} e^{- s t} d t

derivative of y=(((3x^2))/(2x+4))^3 derivative of

y = (\frac{( 3 x ^{2} )}{2 x + 4})^{3}

xdy-ydx=(xy)^{1/2}dx

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

tangent of f(x)=7cos(x),\at ((2pi)/3)tangent of

f (x) = 7 cos (x), at (\frac{2 π}{3})

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(2^x) ?
The derivative of arcsin(2^x) is (ln(2)*2^x)/(sqrt(1-4^x))
What is the first derivative of arcsin(2^x) ?
The first derivative of arcsin(2^x) is (ln(2)*2^x)/(sqrt(1-4^x))