What is the derivative of (t^3)/a ?

The derivative of (t^3)/a is (3t^2)/a

What is the first derivative of (t^3)/a ?

The first derivative of (t^3)/a is (3t^2)/a

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derivative of

\frac{t ^{3}}{a}

\frac{3 t ^{2}}{a}

Solution steps

\frac{d}{d t} (\frac{t ^{3}}{a})

Treat

a

as a constant

Take the constant out:

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

= \frac{1}{a} \frac{d}{d t} (t^{3})

Apply the Power Rule:

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

= \frac{1}{a} \cdot 3 t^{3 - 1}

Simplify

\frac{1}{a} \cdot 3 t^{3 - 1} : \frac{3 t ^{2}}{a}

= \frac{3 t ^{2}}{a}

What is the derivative of (t^3)/a ?
The derivative of (t^3)/a is (3t^2)/a
What is the first derivative of (t^3)/a ?
The first derivative of (t^3)/a is (3t^2)/a