What is the derivative of (410t)/((t^2+5)^3) ?

The derivative of (410t)/((t^2+5)^3) is (2050(-t^2+1))/((t^2+5)^4)

What is the first derivative of (410t)/((t^2+5)^3) ?

The first derivative of (410t)/((t^2+5)^3) is (2050(-t^2+1))/((t^2+5)^4)

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derivative of

\frac{410 t}{( t ^{2} + 5 ) ^{3}}

\frac{2050 ( - t ^{2} + 1 )}{( t ^{2} + 5 ) ^{4}}

Solution steps

\frac{d}{d t} (\frac{410 t}{( t ^{2} + 5 ) ^{3}})

Take the constant out:

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

= 410 \frac{d}{d t} (\frac{t}{( t ^{2} + 5 ) ^{3}})

Apply the Quotient Rule:

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

= 410 \cdot \frac{\frac{d t}{d t} ( t ^{2} + 5 ) ^{3} - \frac{d}{d t} ( ( t ^{2} + 5 ) ^{3} ) t}{( ( t ^{2} + 5 ) ^{3} ) ^{2}}

\frac{d t}{d t} = 1

\frac{d}{d t} ((t^{2} + 5)^{3}) = 6 t (t^{2} + 5)^{2}

= 410 \cdot \frac{1 \cdot ( t ^{2} + 5 ) ^{3} - 6 t ( t ^{2} + 5 ) ^{2} t}{( ( t ^{2} + 5 ) ^{3} ) ^{2}}

Simplify

410 \cdot \frac{1 \cdot ( t ^{2} + 5 ) ^{3} - 6 t ( t ^{2} + 5 ) ^{2} t}{( ( t ^{2} + 5 ) ^{3} ) ^{2}} : \frac{2050 ( - t ^{2} + 1 )}{( t ^{2} + 5 ) ^{4}}

= \frac{2050 ( - t ^{2} + 1 )}{( t ^{2} + 5 ) ^{4}}

What is the derivative of (410t)/((t^2+5)^3) ?
The derivative of (410t)/((t^2+5)^3) is (2050(-t^2+1))/((t^2+5)^4)
What is the first derivative of (410t)/((t^2+5)^3) ?
The first derivative of (410t)/((t^2+5)^3) is (2050(-t^2+1))/((t^2+5)^4)