What is the derivative of 2/(t-3) ?

The derivative of 2/(t-3) is -2/((t-3)^2)

What is the first derivative of 2/(t-3) ?

The first derivative of 2/(t-3) is -2/((t-3)^2)

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derivative of

\frac{2}{t - 3}

- \frac{2}{( t - 3 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{2}{t - 3})

Take the constant out:

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

= 2 \frac{d}{d t} (\frac{1}{t - 3})

Apply exponent rule:

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

= 2 \frac{d}{d t} ((t - 3)^{- 1})

Apply the chain rule:

- \frac{1}{( t - 3 ) ^{2}} \frac{d}{d t} (t - 3)

= - \frac{1}{( t - 3 ) ^{2}} \frac{d}{d t} (t - 3)

\frac{d}{d t} (t - 3) = 1

= 2 (- \frac{1}{( t - 3 ) ^{2}} \cdot 1)

Simplify

2 (- \frac{1}{( t - 3 ) ^{2}} \cdot 1) : - \frac{2}{( t - 3 ) ^{2}}

= - \frac{2}{( t - 3 ) ^{2}}

What is the derivative of 2/(t-3) ?
The derivative of 2/(t-3) is -2/((t-3)^2)
What is the first derivative of 2/(t-3) ?
The first derivative of 2/(t-3) is -2/((t-3)^2)