What is the derivative of (60t+180)/(t+6) ?

The derivative of (60t+180)/(t+6) is (180)/((t+6)^2)

What is the first derivative of (60t+180)/(t+6) ?

The first derivative of (60t+180)/(t+6) is (180)/((t+6)^2)

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derivative of

\frac{60 t + 180}{t + 6}

\frac{180}{( t + 6 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{60 t + 180}{t + 6})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d t} ( 60 t + 180 ) ( t + 6 ) - \frac{d}{d t} ( t + 6 ) ( 60 t + 180 )}{( t + 6 ) ^{2}}

\frac{d}{d t} (60 t + 180) = 60

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

= \frac{60 ( t + 6 ) - 1 \cdot ( 60 t + 180 )}{( t + 6 ) ^{2}}

Simplify

\frac{60 ( t + 6 ) - 1 \cdot ( 60 t + 180 )}{( t + 6 ) ^{2}} : \frac{180}{( t + 6 ) ^{2}}

= \frac{180}{( t + 6 ) ^{2}}

\int_{2}^{3} \frac{x}{x ^{2} + 1} d x

\frac{d}{d x} (x ln (y))

\int - \frac{4}{3}

\frac{\partial}{\partial x} (2 x y + y)

\int_{0}^{1} \frac{x - x}{7} d x

What is the derivative of (60t+180)/(t+6) ?
The derivative of (60t+180)/(t+6) is (180)/((t+6)^2)
What is the first derivative of (60t+180)/(t+6) ?
The first derivative of (60t+180)/(t+6) is (180)/((t+6)^2)