What is the derivative of (t-sqrt(t))/(t^{1/7)} ?

The derivative of (t-sqrt(t))/(t^{1/7)} is (5(sqrt(t)-1))/(14t^{9/14)}+1/(2t^{1/7)}

What is the first derivative of (t-sqrt(t))/(t^{1/7)} ?

The first derivative of (t-sqrt(t))/(t^{1/7)} is (5(sqrt(t)-1))/(14t^{9/14)}+1/(2t^{1/7)}

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derivative of

\frac{t - t}{t ^{\frac{1}{7}}}

\frac{5 ( t - 1 )}{14 t ^{\frac{9}{14}}} + \frac{1}{2 t ^{\frac{1}{7}}}

Solution steps

\frac{d}{d t} (\frac{t - t}{t ^{\frac{1}{7}}})

Simplify

\frac{t - t}{t ^{\frac{1}{7}}} : t^{\frac{5}{14}} (t - 1)

= \frac{d}{d t} (t^{\frac{5}{14}} (t - 1))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t^{\frac{5}{14}}, g = t - 1

= \frac{d}{d t} (t^{\frac{5}{14}}) (t - 1) + \frac{d}{d t} (t - 1) t^{\frac{5}{14}}

\frac{d}{d t} (t^{\frac{5}{14}}) = \frac{5}{14 t ^{\frac{9}{14}}}

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

= \frac{5}{14 t ^{\frac{9}{14}}} (t - 1) + \frac{1}{2 t ^{\frac{1}{2}}} t^{\frac{5}{14}}

Simplify

\frac{5}{14 t ^{\frac{9}{14}}} (t - 1) + \frac{1}{2 t ^{\frac{1}{2}}} t^{\frac{5}{14}} : \frac{5 ( t - 1 )}{14 t ^{\frac{9}{14}}} + \frac{1}{2 t ^{\frac{1}{7}}}

= \frac{5 ( t - 1 )}{14 t ^{\frac{9}{14}}} + \frac{1}{2 t ^{\frac{1}{7}}}

What is the derivative of (t-sqrt(t))/(t^{1/7)} ?
The derivative of (t-sqrt(t))/(t^{1/7)} is (5(sqrt(t)-1))/(14t^{9/14)}+1/(2t^{1/7)}
What is the first derivative of (t-sqrt(t))/(t^{1/7)} ?
The first derivative of (t-sqrt(t))/(t^{1/7)} is (5(sqrt(t)-1))/(14t^{9/14)}+1/(2t^{1/7)}