how to differentiate a function with square root
4,190
Here's a hint:
$$\frac{d}{dx}\sqrt{x} = \frac{d}{dx} x^{\frac{1}{2}}.$$
By power rule, we know that $\frac{d}{dx} x^{\alpha} = \alpha x^{\alpha1}$. 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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Author by
Semsem
Updated on August 01, 2022Comments

Semsem 3 months
Trying to solve
$y =7t^410 \sqrt {t+\frac{10}{t}}$
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 over 8 yearsDo you know the chain rule?
