What is the derivative of (125)/(x^2+25) ?

The derivative of (125)/(x^2+25) is -(250x)/((x^2+25)^2)

What is the first derivative of (125)/(x^2+25) ?

The first derivative of (125)/(x^2+25) is -(250x)/((x^2+25)^2)

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derivative of

\frac{125}{x ^{2} + 25}

- \frac{250 x}{( x ^{2} + 25 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{125}{x ^{2} + 25})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 125 \frac{d}{d x} (\frac{1}{x ^{2} + 25})

Apply exponent rule:

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

= 125 \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

= 125 (- \frac{1}{( x ^{2} + 25 ) ^{2}} \cdot 2 x)

Simplify

125 (- \frac{1}{( x ^{2} + 25 ) ^{2}} \cdot 2 x) : - \frac{250 x}{( x ^{2} + 25 ) ^{2}}

= - \frac{250 x}{( x ^{2} + 25 ) ^{2}}

\frac{d}{d x} (x^{4} - 4 x^{2} + 2)

\frac{\partial}{\partial x} (- (x^{2} + y^{2}))

x \to 1 - lim (2 x + 2)

- 3 x^{2} - 8 x

y^{^{''}} + 8 y^{^{'}} + 16 y = 0

What is the derivative of (125)/(x^2+25) ?
The derivative of (125)/(x^2+25) is -(250x)/((x^2+25)^2)
What is the first derivative of (125)/(x^2+25) ?
The first derivative of (125)/(x^2+25) is -(250x)/((x^2+25)^2)