What is the d/(ds)((2s^2)/((s-6)^3)) ?

The d/(ds)((2s^2)/((s-6)^3)) is (2s(-s-12))/((s-6)^4)

What is the first d/(ds)((2s^2)/((s-6)^3)) ?

The first d/(ds)((2s^2)/((s-6)^3)) is (2s(-s-12))/((s-6)^4)

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\frac{d}{d s} (\frac{2 s ^{2}}{( s - 6 ) ^{3}})

\frac{2 s ( - s - 12 )}{( s - 6 ) ^{4}}

Solution steps

\frac{d}{d s} (\frac{2 s ^{2}}{( s - 6 ) ^{3}})

Take the constant out:

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

= 2 \frac{d}{d s} (\frac{s ^{2}}{( s - 6 ) ^{3}})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{d}{d s} ( s ^{2} ) ( s - 6 ) ^{3} - \frac{d}{d s} ( ( s - 6 ) ^{3} ) s ^{2}}{( ( s - 6 ) ^{3} ) ^{2}}

\frac{d}{d s} (s^{2}) = 2 s

\frac{d}{d s} ((s - 6)^{3}) = 3 (s - 6)^{2}

= 2 \cdot \frac{2 s ( s - 6 ) ^{3} - 3 ( s - 6 ) ^{2} s ^{2}}{( ( s - 6 ) ^{3} ) ^{2}}

Simplify

2 \cdot \frac{2 s ( s - 6 ) ^{3} - 3 ( s - 6 ) ^{2} s ^{2}}{( ( s - 6 ) ^{3} ) ^{2}} : \frac{2 s ( - s - 12 )}{( s - 6 ) ^{4}}

= \frac{2 s ( - s - 12 )}{( s - 6 ) ^{4}}

\frac{1}{t} \frac{d y}{d t} - \frac{1}{1 + t ^{2}} = 0, y (0) = 1

t \to 0 lim (\frac{1}{2} e^{- 2 t})

\frac{\partial}{\partial x} (4 x + 6 y)

\int e^{- (x + y)} d y

\frac{d}{d x} (\frac{2}{2 - cos ( π x )})

What is the d/(ds)((2s^2)/((s-6)^3)) ?
The d/(ds)((2s^2)/((s-6)^3)) is (2s(-s-12))/((s-6)^4)
What is the first d/(ds)((2s^2)/((s-6)^3)) ?
The first d/(ds)((2s^2)/((s-6)^3)) is (2s(-s-12))/((s-6)^4)