What is the derivative of s(t)= 1/5 t^4 ?

The derivative of s(t)= 1/5 t^4 is (4t^3)/5

What is the first derivative of s(t)= 1/5 t^4 ?

The first derivative of s(t)= 1/5 t^4 is (4t^3)/5

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derivative of

s (t) = \frac{1}{5} t^{4}

\frac{4 t ^{3}}{5}

Solution steps

\frac{d}{d t} (\frac{1}{5} t^{4})

Take the constant out:

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

= \frac{1}{5} \frac{d}{d t} (t^{4})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{5} \cdot 4 t^{4 - 1}

Simplify

\frac{1}{5} \cdot 4 t^{4 - 1} : \frac{4 t ^{3}}{5}

= \frac{4 t ^{3}}{5}

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What is the derivative of s(t)= 1/5 t^4 ?
The derivative of s(t)= 1/5 t^4 is (4t^3)/5
What is the first derivative of s(t)= 1/5 t^4 ?
The first derivative of s(t)= 1/5 t^4 is (4t^3)/5