What is the derivative of 5/(25x^2+1) ?

The derivative of 5/(25x^2+1) is -(250x)/((25x^2+1)^2)

What is the first derivative of 5/(25x^2+1) ?

The first derivative of 5/(25x^2+1) is -(250x)/((25x^2+1)^2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (25 x^{2} + 1) = 50 x

= 5 (- \frac{1}{( 25 x ^{2} + 1 ) ^{2}} \cdot 50 x)

Simplify

5 (- \frac{1}{( 25 x ^{2} + 1 ) ^{2}} \cdot 50 x) : - \frac{250 x}{( 25 x ^{2} + 1 ) ^{2}}

= - \frac{250 x}{( 25 x ^{2} + 1 ) ^{2}}

\int \frac{2 t ^{5}}{5} - \frac{2 t ^{2}}{5} - \frac{2 t}{5} d t

\frac{d}{d x} (ln (3^{3 x}))

\int_{0}^{\frac{1}{2}} 5 cos (- 1 (x)) d x

\frac{\partial}{\partial x} (y x)

\frac{\partial}{\partial x} (e^{- \frac{π}{2}})

What is the derivative of 5/(25x^2+1) ?
The derivative of 5/(25x^2+1) is -(250x)/((25x^2+1)^2)
What is the first derivative of 5/(25x^2+1) ?
The first derivative of 5/(25x^2+1) is -(250x)/((25x^2+1)^2)