What is the derivative of s(t)= 5/(\sqrt[4]{t)} ?

The derivative of s(t)= 5/(\sqrt[4]{t)} is -5/(4t^{5/4)}

What is the first derivative of s(t)= 5/(\sqrt[4]{t)} ?

The first derivative of s(t)= 5/(\sqrt[4]{t)} is -5/(4t^{5/4)}

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

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

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

Simplify

5 (- \frac{1}{4} t^{- \frac{1}{4} - 1}) : - \frac{5}{4 t ^{\frac{5}{4}}}

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

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What is the derivative of s(t)= 5/(\sqrt[4]{t)} ?
The derivative of s(t)= 5/(\sqrt[4]{t)} is -5/(4t^{5/4)}
What is the first derivative of s(t)= 5/(\sqrt[4]{t)} ?
The first derivative of s(t)= 5/(\sqrt[4]{t)} is -5/(4t^{5/4)}