What is the derivative of x^2y^3+xe^{xy} ?

The derivative of x^2y^3+xe^{xy} is 2xy^3+3y^2(dy)/(dx)x^2+e^{xy}+e^{xy}x(y+x(dy)/(dx))

What is the first derivative of x^2y^3+xe^{xy} ?

The first derivative of x^2y^3+xe^{xy} is 2xy^3+3y^2(dy)/(dx)x^2+e^{xy}+e^{xy}x(y+x(dy)/(dx))

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Popular >

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

\int (10 x + 0.5) d x

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

\frac{d}{d x} (65536 cos (2 x))

\int (16 x + 4) 8 x^{2} + 4 x d x

(3 x^{2} + 5) e^{4 x}

What is the derivative of x^2y^3+xe^{xy} ?
The derivative of x^2y^3+xe^{xy} is 2xy^3+3y^2(dy)/(dx)x^2+e^{xy}+e^{xy}x(y+x(dy)/(dx))
What is the first derivative of x^2y^3+xe^{xy} ?
The first derivative of x^2y^3+xe^{xy} is 2xy^3+3y^2(dy)/(dx)x^2+e^{xy}+e^{xy}x(y+x(dy)/(dx))