What is the derivative of (5x-x^2/(sqrt(x))-3cot(x)) ?

The derivative of (5x-x^2/(sqrt(x))-3cot(x)) is (5-3x)/(2sqrt(x))+3csc^2(x)

What is the first derivative of (5x-x^2/(sqrt(x))-3cot(x)) ?

The first derivative of (5x-x^2/(sqrt(x))-3cot(x)) is (5-3x)/(2sqrt(x))+3csc^2(x)

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\frac{d}{d x} (\frac{5 x - x ^{2}}{x} - 3 cot (x))

\frac{5 - 3 x}{2 x} + 3 csc^{2} (x)

Solution steps

\frac{d}{d x} (\frac{5 x - x ^{2}}{x} - 3 cot (x))

Simplify

\frac{5 x - x ^{2}}{x} - 3 cot (x) : x (5 - x) - 3 cot (x)

= \frac{d}{d x} (x (5 - x) - 3 cot (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x (5 - x)) - \frac{d}{d x} (3 cot (x))

\frac{d}{d x} (x (5 - x)) = \frac{5 - 3 x}{2 x}

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

= \frac{5 - 3 x}{2 x} - (- 3 csc^{2} (x))

Simplify

= \frac{5 - 3 x}{2 x} + 3 csc^{2} (x)

\int (\frac{( y + 1 )}{y})^{2} d y

\int \frac{1}{x ^{2} \cdot 16 + 9 x ^{2}} d x

\frac{\partial}{\partial x} (\frac{1}{2} ln (y))

\int \frac{2}{x} - 4 e^{x} d x

\frac{\partial}{\partial x} (\frac{3 y}{x ^{5}})

What is the derivative of (5x-x^2/(sqrt(x))-3cot(x)) ?
The derivative of (5x-x^2/(sqrt(x))-3cot(x)) is (5-3x)/(2sqrt(x))+3csc^2(x)
What is the first derivative of (5x-x^2/(sqrt(x))-3cot(x)) ?
The first derivative of (5x-x^2/(sqrt(x))-3cot(x)) is (5-3x)/(2sqrt(x))+3csc^2(x)