how to differentiate a function with square root

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Here's a hint:

$$\frac{d}{dx}\sqrt{x} = \frac{d}{dx} x^{\frac{1}{2}}.$$

By power rule, we know that $\frac{d}{dx} x^{\alpha} = \alpha x^{\alpha-1}$. Applying this for the square root, we have

$$\frac{d}{dx}\sqrt{x} = \frac{1}{2}x^{\frac{1}{2}-1} = \frac{1}{2}x^{-\frac{1}{2}}.$$

Then apply the chain rule and you will get the answer.

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Semsem
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Semsem

Updated on August 01, 2022

Comments

  • Semsem
    Semsem 3 months

    Trying to solve

    $y =7t^4-10 \sqrt {t+\frac{10}{t}}$

    I know how to differentiate down to $7(4t^3)- . . .$ and I know a sqrt is equal to $x^.5$ but cannot figure out how to apply that to the rest of the function. Please help!

    thanks

    • preferred_anon
      preferred_anon over 8 years
      Do you know the chain rule?