What is the derivative of (x-3xsqrt(x))/(sqrt(x)) ?

The derivative of (x-3xsqrt(x))/(sqrt(x)) is (1-3sqrt(x))/(2sqrt(x))-3/2

What is the first derivative of (x-3xsqrt(x))/(sqrt(x)) ?

The first derivative of (x-3xsqrt(x))/(sqrt(x)) is (1-3sqrt(x))/(2sqrt(x))-3/2

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derivative of

\frac{x - 3 x x}{x}

\frac{1 - 3 x}{2 x} - \frac{3}{2}

Solution steps

\frac{d}{d x} (\frac{x - 3 x x}{x})

Simplify

\frac{x - 3 x x}{x} : x (1 - 3 x)

= \frac{d}{d x} (x (1 - 3 x))

Apply the Product Rule:

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

f = x, g = 1 - 3 x

= \frac{d}{d x} (x) (1 - 3 x) + \frac{d}{d x} (1 - 3 x) x

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

\frac{d}{d x} (1 - 3 x) = - \frac{3}{2 x}

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

Simplify

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

= \frac{1 - 3 x}{2 x} - \frac{3}{2}

\frac{d}{d x} (\frac{cos ( x )}{- 2 sin ( 2 x )})

\int \frac{9}{x ^{3}} d x

\frac{\partial}{\partial r} (z)

\frac{d}{d x} (\frac{2}{3} (x + 3)^{\frac{3}{2}})

13 x d x = 127 (92) y d y

What is the derivative of (x-3xsqrt(x))/(sqrt(x)) ?
The derivative of (x-3xsqrt(x))/(sqrt(x)) is (1-3sqrt(x))/(2sqrt(x))-3/2
What is the first derivative of (x-3xsqrt(x))/(sqrt(x)) ?
The first derivative of (x-3xsqrt(x))/(sqrt(x)) is (1-3sqrt(x))/(2sqrt(x))-3/2