What is the derivative of x^3-xy+cos(pi(x+y)) ?

The derivative of x^3-xy+cos(pi(x+y)) is 3x^2-y-x(dy)/(dx)-1-(dy)/(dx)

What is the first derivative of x^3-xy+cos(pi(x+y)) ?

The first derivative of x^3-xy+cos(pi(x+y)) is 3x^2-y-x(dy)/(dx)-1-(dy)/(dx)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (x^{3} - x y + cos (π) (x + y))

3 x^{2} - y - x \frac{d y}{d x} - 1 - \frac{d y}{d x}

Solution steps

\frac{d}{d x} (x^{3} - x y + cos (π) (x + y))

Simplify

x^{3} - x y + cos (π) (x + y) : x^{3} - x y - x - y

= \frac{d}{d x} (x^{3} - x y - x - y)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (x y) - \frac{d x}{d x} - \frac{d y}{d x}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

= 3 x^{2} - (y + x \frac{d y}{d x}) - 1 - \frac{d y}{d x}

Simplify

= 3 x^{2} - y - x \frac{d y}{d x} - 1 - \frac{d y}{d x}

What is the derivative of x^3-xy+cos(pi(x+y)) ?
The derivative of x^3-xy+cos(pi(x+y)) is 3x^2-y-x(dy)/(dx)-1-(dy)/(dx)
What is the first derivative of x^3-xy+cos(pi(x+y)) ?
The first derivative of x^3-xy+cos(pi(x+y)) is 3x^2-y-x(dy)/(dx)-1-(dy)/(dx)