What is the derivative of a(sin(x+xcos(x))) ?

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

What is the first derivative of a(sin(x+xcos(x))) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

a (2 cos (x) - x sin (x))

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

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

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