What is the derivative of y=(3x)/(sin(x)) ?

The derivative of y=(3x)/(sin(x)) is 3(csc(x)-xcot(x)csc(x))

What is the first derivative of y=(3x)/(sin(x)) ?

The first derivative of y=(3x)/(sin(x)) is 3(csc(x)-xcot(x)csc(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = \frac{3 x}{sin ( x )}

3 (csc (x) - x cot (x) csc (x))

Solution steps

\frac{d}{d x} (\frac{3 x}{sin ( x )})

Simplify

\frac{3 x}{sin ( x )} : 3 x csc (x)

= \frac{d}{d x} (3 x csc (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (x csc (x))

Apply the Product Rule:

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

f = x, g = csc (x)

= 3 (\frac{d x}{d x} csc (x) + \frac{d}{d x} (csc (x)) x)

\frac{d x}{d x} = 1

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

= 3 (1 \cdot csc (x) + (- cot (x) csc (x)) x)

Simplify

= 3 (csc (x) - x cot (x) csc (x))

x \to - 1 lim (6 - 3 x)

\frac{\partial}{\partial x} (y)

\int_{0}^{2} [(- x^{2} + 4 x) - x^{2}] d x

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

x \to - 2 lim (\frac{x + 4}{x + 2})

What is the derivative of y=(3x)/(sin(x)) ?
The derivative of y=(3x)/(sin(x)) is 3(csc(x)-xcot(x)csc(x))
What is the first derivative of y=(3x)/(sin(x)) ?
The first derivative of y=(3x)/(sin(x)) is 3(csc(x)-xcot(x)csc(x))