What is the derivative of 7e^xcsc(x) ?

The derivative of 7e^xcsc(x) is 7(e^xcsc(x)-e^xcot(x)csc(x))

What is the first derivative of 7e^xcsc(x) ?

The first derivative of 7e^xcsc(x) is 7(e^xcsc(x)-e^xcot(x)csc(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (7 e^{x} csc (x))

7 (e^{x} csc (x) - e^{x} cot (x) csc (x))

Solution steps

\frac{d}{d x} (7 e^{x} csc (x))

Take the constant out:

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

= 7 \frac{d}{d x} (e^{x} csc (x))

Apply the Product Rule:

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

f = e^{x}, g = csc (x)

= 7 (\frac{d}{d x} (e^{x}) csc (x) + \frac{d}{d x} (csc (x)) e^{x})

\frac{d}{d x} (e^{x}) = e^{x}

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

= 7 (e^{x} csc (x) + (- cot (x) csc (x)) e^{x})

Simplify

= 7 (e^{x} csc (x) - e^{x} cot (x) csc (x))

What is the derivative of 7e^xcsc(x) ?
The derivative of 7e^xcsc(x) is 7(e^xcsc(x)-e^xcot(x)csc(x))
What is the first derivative of 7e^xcsc(x) ?
The first derivative of 7e^xcsc(x) is 7(e^xcsc(x)-e^xcot(x)csc(x))