What is the derivative of ((x-sqrt(x))/(x^{1/5)}) ?

The derivative of ((x-sqrt(x))/(x^{1/5)}) is (3(sqrt(x)-1))/(10x^{7/10)}+1/(2x^{1/5)}

What is the first derivative of ((x-sqrt(x))/(x^{1/5)}) ?

The first derivative of ((x-sqrt(x))/(x^{1/5)}) is (3(sqrt(x)-1))/(10x^{7/10)}+1/(2x^{1/5)}

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\frac{d}{d x} (\frac{( x - x )}{x ^{\frac{1}{5}}})

\frac{3 ( x - 1 )}{10 x ^{\frac{7}{10}}} + \frac{1}{2 x ^{\frac{1}{5}}}

Solution steps

\frac{d}{d x} (\frac{( x - x )}{x ^{\frac{1}{5}}})

Simplify

\frac{( x - x )}{x ^{\frac{1}{5}}} : x^{\frac{3}{10}} (x - 1)

= \frac{d}{d x} (x^{\frac{3}{10}} (x - 1))

Apply the Product Rule:

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

f = x^{\frac{3}{10}}, g = x - 1

= \frac{d}{d x} (x^{\frac{3}{10}}) (x - 1) + \frac{d}{d x} (x - 1) x^{\frac{3}{10}}

\frac{d}{d x} (x^{\frac{3}{10}}) = \frac{3}{10 x ^{\frac{7}{10}}}

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

= \frac{3}{10 x ^{\frac{7}{10}}} (x - 1) + \frac{1}{2 x ^{\frac{1}{2}}} x^{\frac{3}{10}}

Simplify

\frac{3}{10 x ^{\frac{7}{10}}} (x - 1) + \frac{1}{2 x ^{\frac{1}{2}}} x^{\frac{3}{10}} : \frac{3 ( x - 1 )}{10 x ^{\frac{7}{10}}} + \frac{1}{2 x ^{\frac{1}{5}}}

= \frac{3 ( x - 1 )}{10 x ^{\frac{7}{10}}} + \frac{1}{2 x ^{\frac{1}{5}}}

100 - \frac{200}{t ^{2} + 4}

- \frac{5}{x ^{5}}

y^{^{''}} + 25 y = cos (4 t)

x \to 0 lim (2 x cot (3 x))

n = 1 \sum \infty \frac{( n )}{2 ^{n}}

What is the derivative of ((x-sqrt(x))/(x^{1/5)}) ?
The derivative of ((x-sqrt(x))/(x^{1/5)}) is (3(sqrt(x)-1))/(10x^{7/10)}+1/(2x^{1/5)}
What is the first derivative of ((x-sqrt(x))/(x^{1/5)}) ?
The first derivative of ((x-sqrt(x))/(x^{1/5)}) is (3(sqrt(x)-1))/(10x^{7/10)}+1/(2x^{1/5)}