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}

t^{2} \frac{d y}{d t} + t y = 6

n = 0 \sum \infty \frac{n}{3} (\frac{2}{3})^{n}

\int_{1}^{5} \frac{x ^{2} - 1}{x} d x

\int 9 sin^{2} (θ) d θ

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