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

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

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

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

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derivative of

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

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

Solution steps

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

Treat

t

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d a}{d a} = 1

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

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

Simplify

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

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

d er i v a t i v e cos (6 x + 2)

d er i v a t i v e \frac{1}{p}

\frac{d}{d y} (\frac{y}{2 x + 1})

d er i v a t i v e \frac{1}{n}

d er i v a t i v e (3 x^{2} + 7) (6 x + 3)

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