What is the derivative of f(t)=sqrt(t)-1/(sqrt(t)) ?

The derivative of f(t)=sqrt(t)-1/(sqrt(t)) is 1/(2sqrt(t))+1/(2t^{3/2)}

What is the first derivative of f(t)=sqrt(t)-1/(sqrt(t)) ?

The first derivative of f(t)=sqrt(t)-1/(sqrt(t)) is 1/(2sqrt(t))+1/(2t^{3/2)}

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derivative of

f (t) = t - \frac{1}{t}

\frac{1}{2 t} + \frac{1}{2 t ^{\frac{3}{2}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d t} (t) = \frac{1}{2 t}

\frac{d}{d t} (\frac{1}{t}) = - \frac{1}{2 t ^{\frac{3}{2}}}

= \frac{1}{2 t} - (- \frac{1}{2 t ^{\frac{3}{2}}})

Simplify

= \frac{1}{2 t} + \frac{1}{2 t ^{\frac{3}{2}}}

What is the derivative of f(t)=sqrt(t)-1/(sqrt(t)) ?
The derivative of f(t)=sqrt(t)-1/(sqrt(t)) is 1/(2sqrt(t))+1/(2t^{3/2)}
What is the first derivative of f(t)=sqrt(t)-1/(sqrt(t)) ?
The first derivative of f(t)=sqrt(t)-1/(sqrt(t)) is 1/(2sqrt(t))+1/(2t^{3/2)}