What is the derivative of y=csc(x)(x+cot(x)) ?

The derivative of y=csc(x)(x+cot(x)) is -xcot(x)csc(x)-2cot^2(x)csc(x)

What is the first derivative of y=csc(x)(x+cot(x)) ?

The first derivative of y=csc(x)(x+cot(x)) is -xcot(x)csc(x)-2cot^2(x)csc(x)

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derivative of

y = csc (x) (x + cot (x))

- x cot (x) csc (x) - 2 cot^{2} (x) csc (x)

Solution steps

\frac{d}{d x} (csc (x) (x + cot (x)))

Apply the Product Rule:

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

f = csc (x), g = x + cot (x)

= \frac{d}{d x} (csc (x)) (x + cot (x)) + \frac{d}{d x} (x + cot (x)) csc (x)

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

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

= (- cot (x) csc (x)) (x + cot (x)) + (- cot^{2} (x)) csc (x)

Simplify

(- cot (x) csc (x)) (x + cot (x)) + (- cot^{2} (x)) csc (x) : - x cot (x) csc (x) - 2 cot^{2} (x) csc (x)

= - x cot (x) csc (x) - 2 cot^{2} (x) csc (x)

f (x) = x^{5} e^{x}

\frac{\partial}{\partial x} (21 x^{3} cos (7 x^{2} y))

\int \frac{1}{x ^{2} - 16} d x

x \to + 2 - lim (6 - 3 x - 3)

\frac{d}{d x} (x^{1 - x})

What is the derivative of y=csc(x)(x+cot(x)) ?
The derivative of y=csc(x)(x+cot(x)) is -xcot(x)csc(x)-2cot^2(x)csc(x)
What is the first derivative of y=csc(x)(x+cot(x)) ?
The first derivative of y=csc(x)(x+cot(x)) is -xcot(x)csc(x)-2cot^2(x)csc(x)