What is the derivative of G(t)=(4t)/(t+5) ?

The derivative of G(t)=(4t)/(t+5) is (20)/((t+5)^2)

What is the first derivative of G(t)=(4t)/(t+5) ?

The first derivative of G(t)=(4t)/(t+5) is (20)/((t+5)^2)

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derivative of

G (t) = \frac{4 t}{t + 5}

\frac{20}{( t + 5 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{4 t}{t + 5})

Take the constant out:

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

= 4 \frac{d}{d t} (\frac{t}{t + 5})

Apply the Quotient Rule:

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

= 4 \cdot \frac{\frac{d t}{d t} ( t + 5 ) - \frac{d}{d t} ( t + 5 ) t}{( t + 5 ) ^{2}}

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

\frac{d}{d t} (t + 5) = 1

= 4 \cdot \frac{1 \cdot ( t + 5 ) - 1 \cdot t}{( t + 5 ) ^{2}}

Simplify

4 \cdot \frac{1 \cdot ( t + 5 ) - 1 \cdot t}{( t + 5 ) ^{2}} : \frac{20}{( t + 5 ) ^{2}}

= \frac{20}{( t + 5 ) ^{2}}

\frac{d}{d x} (arcsin (3 x - 4 x^{3}))

lo g_{3} (11) p^{3}

y = \frac{5}{x}, (1, 5)

\frac{d}{d x} (\frac{sin ( 2 x )}{1 + cos ( x )})

\frac{\partial}{\partial x} (cos (x y) e^{x^{2}})

What is the derivative of G(t)=(4t)/(t+5) ?
The derivative of G(t)=(4t)/(t+5) is (20)/((t+5)^2)
What is the first derivative of G(t)=(4t)/(t+5) ?
The first derivative of G(t)=(4t)/(t+5) is (20)/((t+5)^2)