What is the derivative of x^e+1/(x^{sqrt(10)}) ?

The derivative of x^e+1/(x^{sqrt(10)}) is ex^{e-1}-sqrt(10)x^{-sqrt(10)-1}

What is the first derivative of x^e+1/(x^{sqrt(10)}) ?

The first derivative of x^e+1/(x^{sqrt(10)}) is ex^{e-1}-sqrt(10)x^{-sqrt(10)-1}

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\frac{d}{d x} (x^{e} + \frac{1}{x ^{10}})

e x^{e - 1} - 10 x^{- 10 - 1}

Solution steps

\frac{d}{d x} (x^{e} + \frac{1}{x ^{10}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{e}) + \frac{d}{d x} (\frac{1}{x ^{10}})

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

\frac{d}{d x} (\frac{1}{x ^{10}}) = - 10 x^{- 10 - 1}

= e x^{e - 1} - 10 x^{- 10 - 1}

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