What is the derivative of (2000t)/(4t+75) ?

The derivative of (2000t)/(4t+75) is (150000)/((4t+75)^2)

What is the first derivative of (2000t)/(4t+75) ?

The first derivative of (2000t)/(4t+75) is (150000)/((4t+75)^2)

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derivative of

\frac{2000 t}{4 t + 75}

\frac{150000}{( 4 t + 75 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{2000 t}{4 t + 75})

Take the constant out:

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

= 2000 \frac{d}{d t} (\frac{t}{4 t + 75})

Apply the Quotient Rule:

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

= 2000 \cdot \frac{\frac{d t}{d t} ( 4 t + 75 ) - \frac{d}{d t} ( 4 t + 75 ) t}{( 4 t + 75 ) ^{2}}

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

\frac{d}{d t} (4 t + 75) = 4

= 2000 \cdot \frac{1 \cdot ( 4 t + 75 ) - 4 t}{( 4 t + 75 ) ^{2}}

Simplify

2000 \cdot \frac{1 \cdot ( 4 t + 75 ) - 4 t}{( 4 t + 75 ) ^{2}} : \frac{150000}{( 4 t + 75 ) ^{2}}

= \frac{150000}{( 4 t + 75 ) ^{2}}

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

\int \frac{15 e ^{5 z}}{e ^{5 z} + 2} d z

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

\int sec^{5} (x) tan (x) d x

f (x) = - \frac{13}{x ^{6}}

What is the derivative of (2000t)/(4t+75) ?
The derivative of (2000t)/(4t+75) is (150000)/((4t+75)^2)
What is the first derivative of (2000t)/(4t+75) ?
The first derivative of (2000t)/(4t+75) is (150000)/((4t+75)^2)