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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!


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Do you know the chain rule? – Daniel Littlewood Feb 27 '14 at 22:43
up vote 0 down vote accepted

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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differentiate the function $\sqrt{f(x)}$ with respect to $f(x)$ just like algebraic function taking exponent $\frac{1}{2}$ and multiply it with the differentiation of $f(x)$ with respect to $x$


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