What is the derivative of x(acos(x+bsin(x))) ?

The derivative of x(acos(x+bsin(x))) is acos(x)+bsin(x)+x(-asin(x)+bcos(x))

What is the first derivative of x(acos(x+bsin(x))) ?

The first derivative of x(acos(x+bsin(x))) is acos(x)+bsin(x)+x(-asin(x)+bcos(x))

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 (a cos (x) + b sin (x)))

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = a cos (x) + b sin (x)

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

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

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

= 1 \cdot (a cos (x) + b sin (x)) + (- a sin (x) + b cos (x)) x

Simplify

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

\int_{- 1}^{e - 2} \frac{t}{t ^{2} + 2} d t

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

\frac{d}{d x} (x co x)

\int 2 x y z^{2} e^{x^{2}} d x

\int (4 x^{3} + 1)^{4} 12 x^{2} d x

What is the derivative of x(acos(x+bsin(x))) ?
The derivative of x(acos(x+bsin(x))) is acos(x)+bsin(x)+x(-asin(x)+bcos(x))
What is the first derivative of x(acos(x+bsin(x))) ?
The first derivative of x(acos(x+bsin(x))) is acos(x)+bsin(x)+x(-asin(x)+bcos(x))