What is the derivative of-e^{xy} ?

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

What is the first derivative of-e^{xy} ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

\frac{d}{d x} (lo g_{2} (x - 1))

\int sin^{2} (x) cos^{3} (d) x d x

\int \frac{1}{2} ln x^{2} + 1 d x

\int sin (3 x) sin (2 x) sin (x) d x

\frac{1}{4} y^{^{''}} + 4 y = 2 tan (4 t) - \frac{1}{3} e^{3 t}

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