What is the derivative of 1/(2t^2+1) ?

The derivative of 1/(2t^2+1) is -(4t)/((2t^2+1)^2)

What is the first derivative of 1/(2t^2+1) ?

The first derivative of 1/(2t^2+1) is -(4t)/((2t^2+1)^2)

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derivative of

\frac{1}{2 t ^{2} + 1}

- \frac{4 t}{( 2 t ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{1}{2 t ^{2} + 1})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d t} (2 t^{2} + 1) = 4 t

= - \frac{1}{( 2 t ^{2} + 1 ) ^{2}} \cdot 4 t

Simplify

- \frac{1}{( 2 t ^{2} + 1 ) ^{2}} \cdot 4 t : - \frac{4 t}{( 2 t ^{2} + 1 ) ^{2}}

= - \frac{4 t}{( 2 t ^{2} + 1 ) ^{2}}

x \to 0 lim (x^{2} + 1)

\int a^{x} e^{x} d x

y^{^{'}} - 5 y = - t

\frac{\partial}{\partial x} (e^{y s i n (x)})

\frac{d}{d x} (4 9 - x)

What is the derivative of 1/(2t^2+1) ?
The derivative of 1/(2t^2+1) is -(4t)/((2t^2+1)^2)
What is the first derivative of 1/(2t^2+1) ?
The first derivative of 1/(2t^2+1) is -(4t)/((2t^2+1)^2)