What is the derivative of 1/(x^2-25) ?

The derivative of 1/(x^2-25) is -(2x)/((x^2-25)^2)

What is the first derivative of 1/(x^2-25) ?

The first derivative of 1/(x^2-25) is -(2x)/((x^2-25)^2)

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\frac{d}{d x} (\frac{1}{x ^{2} - 25})

- \frac{2 x}{( x ^{2} - 25 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{2} - 25})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((x^{2} - 25)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{2} - 25 ) ^{2}} \frac{d}{d x} (x^{2} - 25)

= - \frac{1}{( x ^{2} - 25 ) ^{2}} \frac{d}{d x} (x^{2} - 25)

\frac{d}{d x} (x^{2} - 25) = 2 x

= - \frac{1}{( x ^{2} - 25 ) ^{2}} \cdot 2 x

Simplify

- \frac{1}{( x ^{2} - 25 ) ^{2}} \cdot 2 x : - \frac{2 x}{( x ^{2} - 25 ) ^{2}}

= - \frac{2 x}{( x ^{2} - 25 ) ^{2}}

y^{^{''}} + 25 y = sin (5 x)

\int sec^{2} (x) + 9 d x

\int - \frac{5 ^{- x}}{ln ( 5 )} d x

\int - 36 x^{2} - 18 x - 4 d x

\int (x^{2} - 5 x + 3) d x

What is the derivative of 1/(x^2-25) ?
The derivative of 1/(x^2-25) is -(2x)/((x^2-25)^2)
What is the first derivative of 1/(x^2-25) ?
The first derivative of 1/(x^2-25) is -(2x)/((x^2-25)^2)