What is the derivative of (1-t^4)/4 ?

The derivative of (1-t^4)/4 is -t^3

What is the first derivative of (1-t^4)/4 ?

The first derivative of (1-t^4)/4 is -t^3

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derivative of

\frac{1 - t ^{4}}{4}

- t^{3}

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d t} (1) = 0

\frac{d}{d t} (t^{4}) = 4 t^{3}

= \frac{1}{4} (0 - 4 t^{3})

Simplify

\frac{1}{4} (0 - 4 t^{3}) : - t^{3}

= - t^{3}

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