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

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

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

The first derivative of (sqrt(x)-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}}}

(1 - x)^{\frac{1}{4}}, 0

\int cos (x + \frac{π}{3}) d x

\int_{5}^{6} (\frac{7}{x ^{2}} - 1) d x

\int cos (x) y

- 3 x^{3} - 2 x^{2} - 1

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