Find the derivative.
-$$y = \frac { 1 } { 5 x ^ { 2 } } + \frac { 1 } { 9 x }$$
A) $- \frac { 1 } { 5 x ^ { 3 } } + \frac { 1 } { 9 x ^ { 2 } }$
B) $- \frac { 2 } { 5 x ^ { 3 } } - \frac { 1 } { 9 x ^ { 2 } }$
C) $\frac { 2 } { 5 x ^ { 3 } } + \frac { 1 } { 9 x ^ { 2 } }$
$D ) = \frac { 2 } { 5 x } - \frac { 1 } { 9 x ^ { 2 } }$

Question

Quizplus · Accepted Answer

To find the derivative of $y = \frac { 1 } { 5 x ^ { 2 } } + \frac { 1 } { 9 x }$, we apply the power rule for differentiation. Rewrite the function as $y = \frac{1}{5}x^{-2} + \frac{1}{9}x^{-1}$. Differentiating term by term, we get $\frac{dy}{dx} = -\frac{2}{5}x^{-3} - \frac{1}{9}x^{-2}$, which corresponds to choice B.

Find the Derivative y=15x2+19xy = \frac { 1 } { 5 x ^ { 2 } } + \frac { 1 } { 9 x }y=5x21​+9x1​

Find the Derivative $y = \frac { 1 } { 5 x ^ { 2 } } + \frac { 1 } { 9 x }$