What is the derivative of (490t)/((t^2+7)^3) ?

The derivative of (490t)/((t^2+7)^3) is (490(-5t^2+7))/((t^2+7)^4)

What is the first derivative of (490t)/((t^2+7)^3) ?

The first derivative of (490t)/((t^2+7)^3) is (490(-5t^2+7))/((t^2+7)^4)

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derivative of

\frac{490 t}{( t ^{2} + 7 ) ^{3}}

\frac{490 ( - 5 t ^{2} + 7 )}{( t ^{2} + 7 ) ^{4}}

Solution steps

\frac{d}{d t} (\frac{490 t}{( t ^{2} + 7 ) ^{3}})

Take the constant out:

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

= 490 \frac{d}{d t} (\frac{t}{( t ^{2} + 7 ) ^{3}})

Apply the Quotient Rule:

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

= 490 \cdot \frac{\frac{d t}{d t} ( t ^{2} + 7 ) ^{3} - \frac{d}{d t} ( ( t ^{2} + 7 ) ^{3} ) t}{( ( t ^{2} + 7 ) ^{3} ) ^{2}}

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

\frac{d}{d t} ((t^{2} + 7)^{3}) = 6 t (t^{2} + 7)^{2}

= 490 \cdot \frac{1 \cdot ( t ^{2} + 7 ) ^{3} - 6 t ( t ^{2} + 7 ) ^{2} t}{( ( t ^{2} + 7 ) ^{3} ) ^{2}}

Simplify

490 \cdot \frac{1 \cdot ( t ^{2} + 7 ) ^{3} - 6 t ( t ^{2} + 7 ) ^{2} t}{( ( t ^{2} + 7 ) ^{3} ) ^{2}} : \frac{490 ( - 5 t ^{2} + 7 )}{( t ^{2} + 7 ) ^{4}}

= \frac{490 ( - 5 t ^{2} + 7 )}{( t ^{2} + 7 ) ^{4}}

\frac{d}{d x} (\frac{x ^{2} ( x + 2 ) ^{4}}{( 2 x ^{2} - 1 ) ^{3}})

sin (t - 8)

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

\frac{d}{d x} (6 x^{2} sin (x) tan (x))

\int 1 + (e^{x})^{2} d x

What is the derivative of (490t)/((t^2+7)^3) ?
The derivative of (490t)/((t^2+7)^3) is (490(-5t^2+7))/((t^2+7)^4)
What is the first derivative of (490t)/((t^2+7)^3) ?
The first derivative of (490t)/((t^2+7)^3) is (490(-5t^2+7))/((t^2+7)^4)