What is the derivative of (3x-x^2/(sqrt(x))-4cot(x)) ?

The derivative of (3x-x^2/(sqrt(x))-4cot(x)) is (3-3x)/(2sqrt(x))+4csc^2(x)

What is the first derivative of (3x-x^2/(sqrt(x))-4cot(x)) ?

The first derivative of (3x-x^2/(sqrt(x))-4cot(x)) is (3-3x)/(2sqrt(x))+4csc^2(x)

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\frac{d}{d x} (\frac{3 x - x ^{2}}{x} - 4 cot (x))

\frac{3 - 3 x}{2 x} + 4 csc^{2} (x)

Solution steps

\frac{d}{d x} (\frac{3 x - x ^{2}}{x} - 4 cot (x))

Simplify

\frac{3 x - x ^{2}}{x} - 4 cot (x) : x (3 - x) - 4 cot (x)

= \frac{d}{d x} (x (3 - x) - 4 cot (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x (3 - x)) - \frac{d}{d x} (4 cot (x))

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

\frac{d}{d x} (4 cot (x)) = - 4 csc^{2} (x)

= \frac{3 - 3 x}{2 x} - (- 4 csc^{2} (x))

Simplify

= \frac{3 - 3 x}{2 x} + 4 csc^{2} (x)

What is the derivative of (3x-x^2/(sqrt(x))-4cot(x)) ?
The derivative of (3x-x^2/(sqrt(x))-4cot(x)) is (3-3x)/(2sqrt(x))+4csc^2(x)
What is the first derivative of (3x-x^2/(sqrt(x))-4cot(x)) ?
The first derivative of (3x-x^2/(sqrt(x))-4cot(x)) is (3-3x)/(2sqrt(x))+4csc^2(x)