What is the derivative of 5t^4 ?

The derivative of 5t^4 is 20t^3

What is the first derivative of 5t^4 ?

The first derivative of 5t^4 is 20t^3

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derivative

20 t^{3}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 20 t^{3}