What is the derivative of (x-sqrt(x)/(x^{1/7)}) ?

The derivative of (x-sqrt(x)/(x^{1/7)}) is (5(sqrt(x)-1))/(14x^{9/14)}+1/(2x^{1/7)}

What is the first derivative of (x-sqrt(x)/(x^{1/7)}) ?

The first derivative of (x-sqrt(x)/(x^{1/7)}) is (5(sqrt(x)-1))/(14x^{9/14)}+1/(2x^{1/7)}

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\frac{d}{d x} (\frac{x - x}{x ^{\frac{1}{7}}})

\frac{5 ( x - 1 )}{14 x ^{\frac{9}{14}}} + \frac{1}{2 x ^{\frac{1}{7}}}

Solution steps

\frac{d}{d x} (\frac{x - x}{x ^{\frac{1}{7}}})

Simplify

\frac{x - x}{x ^{\frac{1}{7}}} : x^{\frac{5}{14}} (x - 1)

= \frac{d}{d x} (x^{\frac{5}{14}} (x - 1))

Apply the Product Rule:

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

f = x^{\frac{5}{14}}, g = x - 1

= \frac{d}{d x} (x^{\frac{5}{14}}) (x - 1) + \frac{d}{d x} (x - 1) x^{\frac{5}{14}}

\frac{d}{d x} (x^{\frac{5}{14}}) = \frac{5}{14 x ^{\frac{9}{14}}}

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

= \frac{5}{14 x ^{\frac{9}{14}}} (x - 1) + \frac{1}{2 x ^{\frac{1}{2}}} x^{\frac{5}{14}}

Simplify

\frac{5}{14 x ^{\frac{9}{14}}} (x - 1) + \frac{1}{2 x ^{\frac{1}{2}}} x^{\frac{5}{14}} : \frac{5 ( x - 1 )}{14 x ^{\frac{9}{14}}} + \frac{1}{2 x ^{\frac{1}{7}}}

= \frac{5 ( x - 1 )}{14 x ^{\frac{9}{14}}} + \frac{1}{2 x ^{\frac{1}{7}}}

f (x) = x + 2 \cdot x + 2

\int x^{4} - 2 d x

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\int_{6}^{8} 2 π x (- \frac{3}{2} x + 12) d x

\frac{\partial}{\partial r} (r cos (x))

What is the derivative of (x-sqrt(x)/(x^{1/7)}) ?
The derivative of (x-sqrt(x)/(x^{1/7)}) is (5(sqrt(x)-1))/(14x^{9/14)}+1/(2x^{1/7)}
What is the first derivative of (x-sqrt(x)/(x^{1/7)}) ?
The first derivative of (x-sqrt(x)/(x^{1/7)}) is (5(sqrt(x)-1))/(14x^{9/14)}+1/(2x^{1/7)}