If $f (x) = x^{- \frac{5}{7}}$ $f(x)=x^(-5/7)$ , how do you compute f'(3)?

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Answer 1 · 2018-04-29T22:17:30

$\approx - 0.109$ $~~-0.109$

Here, we can use the Power Rule

$\frac{d}{d x} (x^{a}) = a x^{a - 1}$ $d/dx(x^a)=ax^(a-1)$

If this looks foreign to you, it's really straightforward:

Doing this, we get

$- \frac{5}{7} x^{- \frac{5}{7} - \frac{7}{7}}$ $-5/7x^(-5/7-7/7)$

$=>f'(x)=-5/7x^(-12/7)$

Now, we can plug in $3$ for $x$ to evaluate $f'(3)$ . We get

$f'(3)=-5/7(3)^(-12/7)$

$=>-5/7*(1/3^(12/7))$

which is approximately equal to $-0.109$

Notice, we only used the Power Rule here, stated above, and we evaluated the expression at $3$ .

Hope this helps!

If f(x)=x^(-5/7)f(x)=x−57f(x)=x^(-5/7), how do you compute f'(3)?