What is the derivative of (t-sqrt(t))/(t^{1/8)} ?

The derivative of (t-sqrt(t))/(t^{1/8)} is (3(sqrt(t)-1))/(8t^{5/8)}+1/(2t^{1/8)}

What is the first derivative of (t-sqrt(t))/(t^{1/8)} ?

The first derivative of (t-sqrt(t))/(t^{1/8)} is (3(sqrt(t)-1))/(8t^{5/8)}+1/(2t^{1/8)}

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derivative of

\frac{t - t}{t ^{\frac{1}{8}}}

\frac{3 ( t - 1 )}{8 t ^{\frac{5}{8}}} + \frac{1}{2 t ^{\frac{1}{8}}}

Solution steps

\frac{d}{d t} (\frac{t - t}{t ^{\frac{1}{8}}})

Simplify

\frac{t - t}{t ^{\frac{1}{8}}} : t^{\frac{3}{8}} (t - 1)

= \frac{d}{d t} (t^{\frac{3}{8}} (t - 1))

Apply the Product Rule:

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

f = t^{\frac{3}{8}}, g = t - 1

= \frac{d}{d t} (t^{\frac{3}{8}}) (t - 1) + \frac{d}{d t} (t - 1) t^{\frac{3}{8}}

\frac{d}{d t} (t^{\frac{3}{8}}) = \frac{3}{8 t ^{\frac{5}{8}}}

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

= \frac{3}{8 t ^{\frac{5}{8}}} (t - 1) + \frac{1}{2 t ^{\frac{1}{2}}} t^{\frac{3}{8}}

Simplify

\frac{3}{8 t ^{\frac{5}{8}}} (t - 1) + \frac{1}{2 t ^{\frac{1}{2}}} t^{\frac{3}{8}} : \frac{3 ( t - 1 )}{8 t ^{\frac{5}{8}}} + \frac{1}{2 t ^{\frac{1}{8}}}

= \frac{3 ( t - 1 )}{8 t ^{\frac{5}{8}}} + \frac{1}{2 t ^{\frac{1}{8}}}

(5 e^{2 t} - 3)^{2}

x \to 6 lim (7 x - 6)

y^{^{''}} + y = 2 t cos (t)

y = (4 x^{2} + 5 x)^{2}

\int 2 t^{2} e^{- s t} d t

What is the derivative of (t-sqrt(t))/(t^{1/8)} ?
The derivative of (t-sqrt(t))/(t^{1/8)} is (3(sqrt(t)-1))/(8t^{5/8)}+1/(2t^{1/8)}
What is the first derivative of (t-sqrt(t))/(t^{1/8)} ?
The first derivative of (t-sqrt(t))/(t^{1/8)} is (3(sqrt(t)-1))/(8t^{5/8)}+1/(2t^{1/8)}