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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

5 e^{3} x

arcsin (3^{\frac{1}{2}}) x

(x^{3} + 4 x)^{3}

9 cos^{3} (x)

(2 x^{2} + 9)^{3}

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