What is (\partial)/(\partial x)(x+2^{1/x}) ?

The answer to (\partial)/(\partial x)(x+2^{1/x}) is 1-(ln(2)*2^{1/x})/(x^2)

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(\partial)/(\partial x)(x+2^{1/x})

\frac{\partial}{\partial x} (x + 2^{\frac{1}{x}})

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

Solution steps

\frac{\partial}{\partial x} (x + 2^{\frac{1}{x}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (2^{\frac{1}{x}})

\frac{\partial}{\partial x} (x) = 1

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

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

y^{^{''}} + 6 y^{^{'}} + 8 y = x^{2} e^{- x}

\frac{\partial}{\partial x} (7 e^{x^{2} l n (y)})

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

\int \frac{7}{x ^{2} x ^{2} + 9} d x

\int \frac{1}{y ( 1 - y )} d y

What is (\partial)/(\partial x)(x+2^{1/x}) ?
The answer to (\partial)/(\partial x)(x+2^{1/x}) is 1-(ln(2)*2^{1/x})/(x^2)