What is the derivative of ((1-4t))/((6+t)) ?

The derivative of ((1-4t))/((6+t)) is -(25)/((6+t)^2)

What is the first derivative of ((1-4t))/((6+t)) ?

The first derivative of ((1-4t))/((6+t)) is -(25)/((6+t)^2)

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derivative of

\frac{( 1 - 4 t )}{( 6 + t )}

- \frac{25}{( 6 + t ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{1 - 4 t}{6 + t})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d t} ( 1 - 4 t ) ( 6 + t ) - \frac{d}{d t} ( 6 + t ) ( 1 - 4 t )}{( 6 + t ) ^{2}}

\frac{d}{d t} (1 - 4 t) = - 4

\frac{d}{d t} (6 + t) = 1

= \frac{( - 4 ) ( 6 + t ) - 1 \cdot ( 1 - 4 t )}{( 6 + t ) ^{2}}

Simplify

\frac{( - 4 ) ( 6 + t ) - 1 \cdot ( 1 - 4 t )}{( 6 + t ) ^{2}} : - \frac{25}{( 6 + t ) ^{2}}

= - \frac{25}{( 6 + t ) ^{2}}

\frac{d}{d t} (6)

\frac{d}{d x} (- 5 x e^{- x})

\int 2 sin^{2} (π x) cos^{5} (π x) d x

(- 5, 1), (8, - 5)

ln (2 - 7 x)

What is the derivative of ((1-4t))/((6+t)) ?
The derivative of ((1-4t))/((6+t)) is -(25)/((6+t)^2)
What is the first derivative of ((1-4t))/((6+t)) ?
The first derivative of ((1-4t))/((6+t)) is -(25)/((6+t)^2)