What is the derivative of ((sqrt(t)-3t))/t ?

The derivative of ((sqrt(t)-3t))/t is -1/(2t^{3/2)}

What is the first derivative of ((sqrt(t)-3t))/t ?

The first derivative of ((sqrt(t)-3t))/t is -1/(2t^{3/2)}

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derivative of

\frac{( t - 3 t )}{t}

- \frac{1}{2 t ^{\frac{3}{2}}}

Solution steps

\frac{d}{d t} (\frac{t - 3 t}{t})

Apply the Quotient Rule:

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

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

\frac{d}{d t} (t - 3 t) = \frac{1}{2 t} - 3

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

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

Simplify

\frac{( \frac{1}{2 t} - 3 ) t - 1 \cdot ( t - 3 t )}{t ^{2}} : - \frac{1}{2 t ^{\frac{3}{2}}}

= - \frac{1}{2 t ^{\frac{3}{2}}}

\frac{\partial}{\partial x} (\frac{3 x y}{x ^{2} + y ^{2}})

\int ln (2) d x

e^{- 7 x}, 0

\int arctan^{2} (x) d x

\frac{d}{d x} (cos^{4} (x) + sin^{4} (x))

What is the derivative of ((sqrt(t)-3t))/t ?
The derivative of ((sqrt(t)-3t))/t is -1/(2t^{3/2)}
What is the first derivative of ((sqrt(t)-3t))/t ?
The first derivative of ((sqrt(t)-3t))/t is -1/(2t^{3/2)}