What is the derivative of (450t)/((t^2+6)^3) ?

The derivative of (450t)/((t^2+6)^3) is (450(-5t^2+6))/((t^2+6)^4)

What is the first derivative of (450t)/((t^2+6)^3) ?

The first derivative of (450t)/((t^2+6)^3) is (450(-5t^2+6))/((t^2+6)^4)

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derivative of

\frac{450 t}{( t ^{2} + 6 ) ^{3}}

\frac{450 ( - 5 t ^{2} + 6 )}{( t ^{2} + 6 ) ^{4}}

Solution steps

\frac{d}{d t} (\frac{450 t}{( t ^{2} + 6 ) ^{3}})

Take the constant out:

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

= 450 \frac{d}{d t} (\frac{t}{( t ^{2} + 6 ) ^{3}})

Apply the Quotient Rule:

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

= 450 \cdot \frac{\frac{d t}{d t} ( t ^{2} + 6 ) ^{3} - \frac{d}{d t} ( ( t ^{2} + 6 ) ^{3} ) t}{( ( t ^{2} + 6 ) ^{3} ) ^{2}}

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

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

= 450 \cdot \frac{1 \cdot ( t ^{2} + 6 ) ^{3} - 6 t ( t ^{2} + 6 ) ^{2} t}{( ( t ^{2} + 6 ) ^{3} ) ^{2}}

Simplify

450 \cdot \frac{1 \cdot ( t ^{2} + 6 ) ^{3} - 6 t ( t ^{2} + 6 ) ^{2} t}{( ( t ^{2} + 6 ) ^{3} ) ^{2}} : \frac{450 ( - 5 t ^{2} + 6 )}{( t ^{2} + 6 ) ^{4}}

= \frac{450 ( - 5 t ^{2} + 6 )}{( t ^{2} + 6 ) ^{4}}

y = \frac{2 x}{x ^{2} + 1}, (0, 0)

\frac{\partial}{\partial y} (x y e^{y})

\int \frac{2 y}{1 - y ^{2}} d y

g (x) = x e^{x}

\int \frac{4}{x ^{2}} - \frac{7}{x ^{5}} d x

What is the derivative of (450t)/((t^2+6)^3) ?
The derivative of (450t)/((t^2+6)^3) is (450(-5t^2+6))/((t^2+6)^4)
What is the first derivative of (450t)/((t^2+6)^3) ?
The first derivative of (450t)/((t^2+6)^3) is (450(-5t^2+6))/((t^2+6)^4)