What is the derivative of x^2+e^{2xy} ?

The derivative of x^2+e^{2xy} is 2x+e^{2xy}*2(y+x(dy)/(dx))

What is the first derivative of x^2+e^{2xy} ?

The first derivative of x^2+e^{2xy} is 2x+e^{2xy}*2(y+x(dy)/(dx))

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\frac{d}{d x} (x^{2} + e^{2 x y})

2 x + e^{2 x y} \cdot 2 (y + x \frac{d y}{d x})

Solution steps

\frac{d}{d x} (x^{2} + e^{2 x y})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{2}) + \frac{d}{d x} (e^{2 x y})

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

\frac{d}{d x} (e^{2 x y}) = e^{2 x y} \cdot 2 (y + x \frac{d y}{d x})

= 2 x + e^{2 x y} \cdot 2 (y + x \frac{d y}{d x})

What is the derivative of x^2+e^{2xy} ?
The derivative of x^2+e^{2xy} is 2x+e^{2xy}*2(y+x(dy)/(dx))
What is the first derivative of x^2+e^{2xy} ?
The first derivative of x^2+e^{2xy} is 2x+e^{2xy}*2(y+x(dy)/(dx))