What is the derivative of (x-9xsqrt(x))/(sqrt(x)) ?

The derivative of (x-9xsqrt(x))/(sqrt(x)) is (1-9sqrt(x))/(2sqrt(x))-9/2

What is the first derivative of (x-9xsqrt(x))/(sqrt(x)) ?

The first derivative of (x-9xsqrt(x))/(sqrt(x)) is (1-9sqrt(x))/(2sqrt(x))-9/2

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derivative of

\frac{x - 9 x x}{x}

\frac{1 - 9 x}{2 x} - \frac{9}{2}

Solution steps

\frac{d}{d x} (\frac{x - 9 x x}{x})

Simplify

\frac{x - 9 x x}{x} : x (1 - 9 x)

= \frac{d}{d x} (x (1 - 9 x))

Apply the Product Rule:

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

f = x, g = 1 - 9 x

= \frac{d}{d x} (x) (1 - 9 x) + \frac{d}{d x} (1 - 9 x) x

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

\frac{d}{d x} (1 - 9 x) = - \frac{9}{2 x}

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

Simplify

\frac{1}{2 x} (1 - 9 x) + (- \frac{9}{2 x}) x : \frac{1 - 9 x}{2 x} - \frac{9}{2}

= \frac{1 - 9 x}{2 x} - \frac{9}{2}

y (2 x + x^{2} cot (x)) d x + x^{2} (1 + y) d y = 0

e^{3 x}

(2 x^{2} + 5) (4 x - 1)

\int \frac{5 - 50 x}{81 - 25 x ^{2}} d x

\int \frac{2 x ^{2}}{x} d x

What is the derivative of (x-9xsqrt(x))/(sqrt(x)) ?
The derivative of (x-9xsqrt(x))/(sqrt(x)) is (1-9sqrt(x))/(2sqrt(x))-9/2
What is the first derivative of (x-9xsqrt(x))/(sqrt(x)) ?
The first derivative of (x-9xsqrt(x))/(sqrt(x)) is (1-9sqrt(x))/(2sqrt(x))-9/2