What is the derivative of (cos(t))/(t^7) ?

The derivative of (cos(t))/(t^7) is -(tsin(t)+7cos(t))/(t^8)

What is the first derivative of (cos(t))/(t^7) ?

The first derivative of (cos(t))/(t^7) is -(tsin(t)+7cos(t))/(t^8)

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derivative of

\frac{cos ( t )}{t ^{7}}

- \frac{t sin ( t ) + 7 cos ( t )}{t ^{8}}

Solution steps

\frac{d}{d t} (\frac{cos ( t )}{t ^{7}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d t} ( cos ( t ) ) t ^{7} - \frac{d}{d t} ( t ^{7} ) cos ( t )}{( t ^{7} ) ^{2}}

\frac{d}{d t} (cos (t)) = - sin (t)

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

= \frac{( - sin ( t ) ) t ^{7} - 7 t ^{6} cos ( t )}{( t ^{7} ) ^{2}}

Simplify

\frac{( - sin ( t ) ) t ^{7} - 7 t ^{6} cos ( t )}{( t ^{7} ) ^{2}} : - \frac{t sin ( t ) + 7 cos ( t )}{t ^{8}}

= - \frac{t sin ( t ) + 7 cos ( t )}{t ^{8}}

What is the derivative of (cos(t))/(t^7) ?
The derivative of (cos(t))/(t^7) is -(tsin(t)+7cos(t))/(t^8)
What is the first derivative of (cos(t))/(t^7) ?
The first derivative of (cos(t))/(t^7) is -(tsin(t)+7cos(t))/(t^8)