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) = \frac{2 x}{7 x ^{2} + 1}

\int 7^{x} cot^{2} (7^{x}) d x

x^{6} + y^{5} x^{7} + 4 \frac{d y}{d x} = 0

\frac{d y}{d x} = - \frac{2 x y}{x ^{2} + 36}

\frac{d}{d x} (arcsec (18 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)