What is the derivative of 2xcsc(xsec(x)) ?

The derivative of 2xcsc(xsec(x)) is 2(2csc(2x)+x(-csc^2(x)+sec^2(x)))

What is the first derivative of 2xcsc(xsec(x)) ?

The first derivative of 2xcsc(xsec(x)) is 2(2csc(2x)+x(-csc^2(x)+sec^2(x)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (2 x csc (x) sec (x))

2 (2 csc (2 x) + x (- csc^{2} (x) + sec^{2} (x)))

Solution steps

\frac{d}{d x} (2 x csc (x) sec (x))

Take the constant out:

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

= 2 \frac{d}{d x} (x csc (x) sec (x))

Apply the Product Rule:

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

f = x, g = csc (x) sec (x)

= 2 (\frac{d x}{d x} csc (x) sec (x) + \frac{d}{d x} (csc (x) sec (x)) x)

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

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

= 2 (1 \cdot csc (x) sec (x) + (- csc^{2} (x) + sec^{2} (x)) x)

Simplify

2 (1 \cdot csc (x) sec (x) + (- csc^{2} (x) + sec^{2} (x)) x) : 2 (2 csc (2 x) + x (- csc^{2} (x) + sec^{2} (x)))

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

What is the derivative of 2xcsc(xsec(x)) ?
The derivative of 2xcsc(xsec(x)) is 2(2csc(2x)+x(-csc^2(x)+sec^2(x)))
What is the first derivative of 2xcsc(xsec(x)) ?
The first derivative of 2xcsc(xsec(x)) is 2(2csc(2x)+x(-csc^2(x)+sec^2(x)))