What is the derivative of e^{xy}cos(x+y) ?

The derivative of e^{xy}cos(x+y) is e^{xy}cos(x+y)(y+x(dy)/(dx))-e^{xy}sin(x+y)(1+(dy)/(dx))

What is the first derivative of e^{xy}cos(x+y) ?

The first derivative of e^{xy}cos(x+y) is e^{xy}cos(x+y)(y+x(dy)/(dx))-e^{xy}sin(x+y)(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} (e^{x y} cos (x + y))

e^{x y} cos (x + y) (y + x \frac{d y}{d x}) - e^{x y} sin (x + y) (1 + \frac{d y}{d x})

Solution steps

\frac{d}{d x} (e^{x y} cos (x + y))

Apply the Product Rule:

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

f = e^{x y}, g = cos (x + y)

= \frac{d}{d x} (e^{x y}) cos (x + y) + \frac{d}{d x} (cos (x + y)) e^{x y}

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

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

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

Simplify

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

What is the derivative of e^{xy}cos(x+y) ?
The derivative of e^{xy}cos(x+y) is e^{xy}cos(x+y)(y+x(dy)/(dx))-e^{xy}sin(x+y)(1+(dy)/(dx))
What is the first derivative of e^{xy}cos(x+y) ?
The first derivative of e^{xy}cos(x+y) is e^{xy}cos(x+y)(y+x(dy)/(dx))-e^{xy}sin(x+y)(1+(dy)/(dx))