What is (\partial)/(\partial x)(3x^2*e^{x^2y}) ?

The answer to (\partial)/(\partial x)(3x^2*e^{x^2y}) is 3(2e^{x^2y}x+2e^{x^2y}x^3y)

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(\partial)/(\partial x)(3x^2*e^{x^2y})

\frac{\partial}{\partial x} (3 x^{2} \cdot e^{x^{2} y})

3 (2 e^{x^{2} y} x + 2 e^{x^{2} y} x^{3} y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{2}, g = e^{x^{2} y}

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

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

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

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

e^{x^{2} y} \cdot 2 y x x^{2} = 2 e^{x^{2} y} x^{3} y

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

cos ((2 x^{2} + 1)^{7})

\frac{d}{d x} (\frac{2 x ^{5} + 5}{x ^{3}})

\frac{1}{2 r} + \frac{1}{5 r ^{\frac{4}{5}}}

\int \frac{- x}{1 - 0.5 x} d x

\frac{\partial}{\partial x} (2 x^{2} - 4 x y + y^{4})

What is (\partial)/(\partial x)(3x^2*e^{x^2y}) ?
The answer to (\partial)/(\partial x)(3x^2*e^{x^2y}) is 3(2e^{x^2y}x+2e^{x^2y}x^3y)