What is the derivative of s(t)=(400t)/((t^{2+5))^3} ?

The derivative of s(t)=(400t)/((t^{2+5))^3} is -(8000)/(t^{21)}

What is the first derivative of s(t)=(400t)/((t^{2+5))^3} ?

The first derivative of s(t)=(400t)/((t^{2+5))^3} is -(8000)/(t^{21)}

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derivative of

s (t) = \frac{400 t}{( t ^{2 + 5} ) ^{3}}

- \frac{8000}{t ^{21}}

Solution steps

\frac{d}{d t} (\frac{400 t}{( t ^{2 + 5} ) ^{3}})

Take the constant out:

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

= 400 \frac{d}{d t} (\frac{t}{( t ^{2 + 5} ) ^{3}})

Apply the Quotient Rule:

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

= 400 \cdot \frac{\frac{d t}{d t} ( t ^{2 + 5} ) ^{3} - \frac{d}{d t} ( ( t ^{2 + 5} ) ^{3} ) t}{( ( t ^{2 + 5} ) ^{3} ) ^{2}}

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

\frac{d}{d t} ((t^{2 + 5})^{3}) = 21 t^{20}

= 400 \cdot \frac{1 \cdot ( t ^{2 + 5} ) ^{3} - 21 t ^{20} t}{( ( t ^{2 + 5} ) ^{3} ) ^{2}}

Simplify

400 \cdot \frac{1 \cdot ( t ^{2 + 5} ) ^{3} - 21 t ^{20} t}{( ( t ^{2 + 5} ) ^{3} ) ^{2}} : - \frac{8000}{t ^{21}}

= - \frac{8000}{t ^{21}}

x \to 4 lim (15)

\frac{d y}{d x} = \frac{( x + y )}{6}

\frac{\partial}{\partial x} (yz)

x \to - 1 lim (2 x + 1)

(x, y) \to (0, 0) lim (\frac{( x y ^{4} )}{x ^{4} + y ^{4}})

What is the derivative of s(t)=(400t)/((t^{2+5))^3} ?
The derivative of s(t)=(400t)/((t^{2+5))^3} is -(8000)/(t^{21)}
What is the first derivative of s(t)=(400t)/((t^{2+5))^3} ?
The first derivative of s(t)=(400t)/((t^{2+5))^3} is -(8000)/(t^{21)}