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son4ous [18]
3 years ago
9

Differentiate

rmula1" title=" \sqrt{x} + \frac{1}{5x} - 3" alt=" \sqrt{x} + \frac{1}{5x} - 3" align="absmiddle" class="latex-formula">
with respect to their variable ​
Mathematics
1 answer:
Leviafan [203]3 years ago
3 0

\\ \tt\longmapsto \dfrac{d}{dx}\sqrt{x}+\dfrac{1}{5x}-3

\\ \tt\longmapsto \dfrac{d}{dx}x^{\frac{1}{2}}+5x^{-1}-3

  • Derivative of any constant is 0

\\ \tt\longmapsto \dfrac{d}{dx}x^{\frac{1}{2}}+5x^{-1}

\boxed{\sf \dfrac{d(x^n)}{dx}=nx^{n-1}}

\\ \tt\longmapsto \dfrac{1}{2}x^{\frac{-1}{2}}-5x^{-2}

\\ \tt\longmapsto \dfrac{x}{2}^{\frac{-1}{2}}-\dfrac{1}{5x^2}

\\ \tt\longmapsto -\sqrt{\dfrac{x}{2}}-\dfrac{1}{5x^2}

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Okay let's get cracking :D

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