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

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

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

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

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derivative of

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

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\frac{5}{2} x^{\frac{5}{2}}

f (x) = 2 x^{4} - 10 x^{2}, at x = - 2

\frac{d}{d x} (ln (x - \frac{π}{2}))

x \to \infty lim (42 + x)

y^{^{'}} + y = x + 5

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