What is the derivative of (x-5xsqrt(x)/(sqrt(x))) ?

The derivative of (x-5xsqrt(x)/(sqrt(x))) is (1-5sqrt(x))/(2sqrt(x))-5/2

What is the first derivative of (x-5xsqrt(x)/(sqrt(x))) ?

The first derivative of (x-5xsqrt(x)/(sqrt(x))) is (1-5sqrt(x))/(2sqrt(x))-5/2

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

\frac{1 - 5 x}{2 x} - \frac{5}{2}

Solution steps

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

Simplify

\frac{x - 5 x x}{x} : x (1 - 5 x)

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

Apply the Product Rule:

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

f = x, g = 1 - 5 x

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

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

\frac{d}{d x} (1 - 5 x) = - \frac{5}{2 x}

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

Simplify

\frac{1}{2 x} (1 - 5 x) + (- \frac{5}{2 x}) x : \frac{1 - 5 x}{2 x} - \frac{5}{2}

= \frac{1 - 5 x}{2 x} - \frac{5}{2}

What is the derivative of (x-5xsqrt(x)/(sqrt(x))) ?
The derivative of (x-5xsqrt(x)/(sqrt(x))) is (1-5sqrt(x))/(2sqrt(x))-5/2
What is the first derivative of (x-5xsqrt(x)/(sqrt(x))) ?
The first derivative of (x-5xsqrt(x)/(sqrt(x))) is (1-5sqrt(x))/(2sqrt(x))-5/2