What is the derivative of (4t)/(4+sqrt(t)) ?

The derivative of (4t)/(4+sqrt(t)) is (2(sqrt(t)+8))/((4+sqrt(t))^2)

What is the first derivative of (4t)/(4+sqrt(t)) ?

The first derivative of (4t)/(4+sqrt(t)) is (2(sqrt(t)+8))/((4+sqrt(t))^2)

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derivative of

\frac{4 t}{4 + t}

\frac{2 ( t + 8 )}{( 4 + t ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{4 t}{4 + t})

Take the constant out:

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

= 4 \frac{d}{d t} (\frac{t}{4 + t})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

4 \cdot \frac{1 \cdot ( 4 + t ) - \frac{1}{2 t} t}{( 4 + t ) ^{2}} : \frac{2 ( t + 8 )}{( 4 + t ) ^{2}}

= \frac{2 ( t + 8 )}{( 4 + t ) ^{2}}

x \to 4 lim (x + 4)

\int - 2 x ln (x) d x

\int - 2 x^{3} d x

\frac{d}{d x} (2 arctan (x))

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

What is the derivative of (4t)/(4+sqrt(t)) ?
The derivative of (4t)/(4+sqrt(t)) is (2(sqrt(t)+8))/((4+sqrt(t))^2)
What is the first derivative of (4t)/(4+sqrt(t)) ?
The first derivative of (4t)/(4+sqrt(t)) is (2(sqrt(t)+8))/((4+sqrt(t))^2)