What is the derivative of-(170t)/((t+4)^2) ?

The derivative of-(170t)/((t+4)^2) is -(170(4-t))/((t+4)^3)

What is the first derivative of-(170t)/((t+4)^2) ?

The first derivative of-(170t)/((t+4)^2) is -(170(4-t))/((t+4)^3)

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derivative of

- \frac{170 t}{( t + 4 ) ^{2}}

- \frac{170 ( 4 - t )}{( t + 4 ) ^{3}}

Solution steps

\frac{d}{d t} (- \frac{170 t}{( t + 4 ) ^{2}})

Take the constant out:

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

= - 170 \frac{d}{d t} (\frac{t}{( t + 4 ) ^{2}})

Apply the Quotient Rule:

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

= - 170 \cdot \frac{\frac{d t}{d t} ( t + 4 ) ^{2} - \frac{d}{d t} ( ( t + 4 ) ^{2} ) t}{( ( t + 4 ) ^{2} ) ^{2}}

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

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

= - 170 \cdot \frac{1 \cdot ( t + 4 ) ^{2} - 2 ( t + 4 ) t}{( ( t + 4 ) ^{2} ) ^{2}}

Simplify

- 170 \cdot \frac{1 \cdot ( t + 4 ) ^{2} - 2 ( t + 4 ) t}{( ( t + 4 ) ^{2} ) ^{2}} : - \frac{170 ( 4 - t )}{( t + 4 ) ^{3}}

= - \frac{170 ( 4 - t )}{( t + 4 ) ^{3}}

x \to 1 + lim (\frac{3}{1 - x})

\frac{d y}{d x} = 3 x + x y

9 y^{^{''}} + 12 y^{^{'}} + 4 y = 0

\int_{0}^{1} (3 x + 1)^{4} d x

f (x) = \frac{1}{1 + x ^{2}}, at x = 2

What is the derivative of-(170t)/((t+4)^2) ?
The derivative of-(170t)/((t+4)^2) is -(170(4-t))/((t+4)^3)
What is the first derivative of-(170t)/((t+4)^2) ?
The first derivative of-(170t)/((t+4)^2) is -(170(4-t))/((t+4)^3)