What is the derivative of e^{x+y}sin(x-y) ?

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

(x - 2) (x - 3)^{2}

\int - \frac{2 ln ( x )}{x ^{2}} d x

\frac{d}{d x} (ln (\frac{x ^{2}}{( x - 4 )}))

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

f (x) = (3 x - 2)^{4}

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