What is the derivative of (t-sqrt(t))/(t^{1/4)} ?

The derivative of (t-sqrt(t))/(t^{1/4)} is (sqrt(t)-1)/(4t^{3/4)}+1/(2t^{1/4)}

What is the first derivative of (t-sqrt(t))/(t^{1/4)} ?

The first derivative of (t-sqrt(t))/(t^{1/4)} is (sqrt(t)-1)/(4t^{3/4)}+1/(2t^{1/4)}

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derivative of

\frac{t - t}{t ^{\frac{1}{4}}}

\frac{t - 1}{4 t ^{\frac{3}{4}}} + \frac{1}{2 t ^{\frac{1}{4}}}

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

f = t^{\frac{1}{4}}, g = t - 1

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

\frac{d}{d t} (t^{\frac{1}{4}}) = \frac{1}{4 t ^{\frac{3}{4}}}

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

= \frac{1}{4 t ^{\frac{3}{4}}} (t - 1) + \frac{1}{2 t ^{\frac{1}{2}}} t^{\frac{1}{4}}

Simplify

\frac{1}{4 t ^{\frac{3}{4}}} (t - 1) + \frac{1}{2 t ^{\frac{1}{2}}} t^{\frac{1}{4}} : \frac{t - 1}{4 t ^{\frac{3}{4}}} + \frac{1}{2 t ^{\frac{1}{4}}}

= \frac{t - 1}{4 t ^{\frac{3}{4}}} + \frac{1}{2 t ^{\frac{1}{4}}}

f (\frac{1}{2}) = 10 + 12 x - 3 x^{2} - x^{3}

x \to 1 lim (\frac{x ^{3 a} - 3 a x + 3 a - 1}{( x - 1 ) ^{2}})

\frac{d}{d t} (4 t^{2} + 3 t - 10)

13 e^{x^{2}}

What is the derivative of (t-sqrt(t))/(t^{1/4)} ?
The derivative of (t-sqrt(t))/(t^{1/4)} is (sqrt(t)-1)/(4t^{3/4)}+1/(2t^{1/4)}
What is the first derivative of (t-sqrt(t))/(t^{1/4)} ?
The first derivative of (t-sqrt(t))/(t^{1/4)} is (sqrt(t)-1)/(4t^{3/4)}+1/(2t^{1/4)}