How do you find the slope of a tangent line to the graph of the function $f (x) = - \frac{5}{x^{3}}$ $f(x)= -5/x^3$ at x=9?

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Answer 1 · 2016-11-27T00:58:19

$f'(9)=5/2187$

$f(x)=frac{-5}{x^3}$

We want to find $f'(9)$ , which is the slope of the tangent line at $x=9$ .

Rewritten with a negative exponent:
$f(x)=-5x^(-3)$

Use the power rule to differentiate:
$f'(x)=(-3)(-5)(x^(-4))$
$f'(x)=15x^(-4)$

$f'(x)=frac{15}{x^4}$

Plug in 9 to find $f'(9)$ :
$f'(9)=frac{15}{(9)^4}$
$f'(9)=15/6561$

$f'(9)=5/2187$

How do you find the slope of a tangent line to the graph of the function f(x)= -5/x^3f(x)=−5x3 f(x)= -5/x^3 at x=9?