What is the d/(dt)(sqrt(5t)+(sqrt(7))/t) ?

The d/(dt)(sqrt(5t)+(sqrt(7))/t) is (sqrt(5)t^{3/2}-2sqrt(7))/(2t^{3/2)sqrt(t)}

What is the first d/(dt)(sqrt(5t)+(sqrt(7))/t) ?

The first d/(dt)(sqrt(5t)+(sqrt(7))/t) is (sqrt(5)t^{3/2}-2sqrt(7))/(2t^{3/2)sqrt(t)}

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\frac{d}{d t} (5 t + \frac{7}{t})

\frac{5 t ^{\frac{3}{2}} - 2 7}{2 t ^{\frac{3}{2}} t}

Solution steps

\frac{d}{d t} (5 t + \frac{7}{t})

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (5 t) + \frac{d}{d t} (\frac{7}{t})

\frac{d}{d t} (5 t) = \frac{5}{2 t}

\frac{d}{d t} (\frac{7}{t}) = - \frac{7}{t ^{2}}

= \frac{5}{2 t} - \frac{7}{t ^{2}}

Simplify

\frac{5}{2 t} - \frac{7}{t ^{2}} : \frac{5 t ^{\frac{3}{2}} - 2 7}{2 t ^{\frac{3}{2}} t}

= \frac{5 t ^{\frac{3}{2}} - 2 7}{2 t ^{\frac{3}{2}} t}

What is the d/(dt)(sqrt(5t)+(sqrt(7))/t) ?
The d/(dt)(sqrt(5t)+(sqrt(7))/t) is (sqrt(5)t^{3/2}-2sqrt(7))/(2t^{3/2)sqrt(t)}
What is the first d/(dt)(sqrt(5t)+(sqrt(7))/t) ?
The first d/(dt)(sqrt(5t)+(sqrt(7))/t) is (sqrt(5)t^{3/2}-2sqrt(7))/(2t^{3/2)sqrt(t)}