What is the derivative of 5/(x^2+25) ?

The derivative of 5/(x^2+25) is -(10x)/((x^2+25)^2)

What is the first derivative of 5/(x^2+25) ?

The first derivative of 5/(x^2+25) is -(10x)/((x^2+25)^2)

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\frac{d}{d x} (\frac{5}{x ^{2} + 25})

- \frac{10 x}{( x ^{2} + 25 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5}{x ^{2} + 25})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{1}{x ^{2} + 25})

Apply exponent rule:

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

= 5 \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

= 5 (- \frac{1}{( x ^{2} + 25 ) ^{2}} \cdot 2 x)

Simplify

5 (- \frac{1}{( x ^{2} + 25 ) ^{2}} \cdot 2 x) : - \frac{10 x}{( x ^{2} + 25 ) ^{2}}

= - \frac{10 x}{( x ^{2} + 25 ) ^{2}}

\int 5 sin (x) 5 - cos (x) d x

\int_{0}^{4} \frac{1}{x ^{2} + x - 6} d x

\int_{1}^{4} (4 x^{2} + x) d x

\int \frac{1}{1 - 5 t} d t

\frac{\partial}{\partial x} (x^{3} \cdot 4 x + 5 y)

What is the derivative of 5/(x^2+25) ?
The derivative of 5/(x^2+25) is -(10x)/((x^2+25)^2)
What is the first derivative of 5/(x^2+25) ?
The first derivative of 5/(x^2+25) is -(10x)/((x^2+25)^2)