What is the derivative of (x-sin(x)(x+cos(x))) ?

The derivative of (x-sin(x)(x+cos(x))) is cos(x)-sin(x)+2x-xcos(x)-xsin(x)-cos(2x)

What is the first derivative of (x-sin(x)(x+cos(x))) ?

The first derivative of (x-sin(x)(x+cos(x))) is cos(x)-sin(x)+2x-xcos(x)-xsin(x)-cos(2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} ((x - sin (x)) (x + cos (x)))

cos (x) - sin (x) + 2 x - x cos (x) - x sin (x) - cos (2 x)

Solution steps

\frac{d}{d x} ((x - sin (x)) (x + cos (x)))

Apply the Product Rule:

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

f = x - sin (x), g = x + cos (x)

= \frac{d}{d x} (x - sin (x)) (x + cos (x)) + \frac{d}{d x} (x + cos (x)) (x - sin (x))

\frac{d}{d x} (x - sin (x)) = 1 - cos (x)

\frac{d}{d x} (x + cos (x)) = 1 - sin (x)

= (1 - cos (x)) (x + cos (x)) + (1 - sin (x)) (x - sin (x))

Simplify

(1 - cos (x)) (x + cos (x)) + (1 - sin (x)) (x - sin (x)) : cos (x) - sin (x) + 2 x - x cos (x) - x sin (x) - cos (2 x)

= cos (x) - sin (x) + 2 x - x cos (x) - x sin (x) - cos (2 x)

2 x \frac{d y}{d x} + y^{3} e^{- 2 x} = 2 x y

\int e^{x} \frac{1}{x} d x

cos (x y)

\frac{\partial}{\partial x} (- 10 x e^{- 5 x^{2} - 2 y^{2}})

\int 6 x + 2 d x

What is the derivative of (x-sin(x)(x+cos(x))) ?
The derivative of (x-sin(x)(x+cos(x))) is cos(x)-sin(x)+2x-xcos(x)-xsin(x)-cos(2x)
What is the first derivative of (x-sin(x)(x+cos(x))) ?
The first derivative of (x-sin(x)(x+cos(x))) is cos(x)-sin(x)+2x-xcos(x)-xsin(x)-cos(2x)