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

The answer to (\partial)/(\partial x)(3(x-y)*e^{3y+2x^2}) is 3(e^{3y+2x^2}+4e^{3y+2x^2}x(x-y))

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

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

3 (e^{3 y + 2 x^{2}} + 4 e^{3 y + 2 x^{2}} x (x - y))

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x - y, g = e^{3 y + 2 x^{2}}

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

\frac{\partial}{\partial x} (x - y) = 1

\frac{\partial}{\partial x} (e^{3 y + 2 x^{2}}) = e^{3 y + 2 x^{2}} \cdot 4 x

= 3 (1 \cdot e^{3 y + 2 x^{2}} + e^{3 y + 2 x^{2}} \cdot 4 x (x - y))

Simplify

= 3 (e^{3 y + 2 x^{2}} + 4 e^{3 y + 2 x^{2}} x (x - y))

\frac{t}{1 + t ^{2}}

\int \frac{x ^{4}}{4 x ^{2} + 1} d x

\int_{1}^{2} (x^{2} + 3 x^{4}) d x

x^{2} + 1, x, [- 1, 2]

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

What is (\partial)/(\partial x)(3(x-y)*e^{3y+2x^2}) ?
The answer to (\partial)/(\partial x)(3(x-y)*e^{3y+2x^2}) is 3(e^{3y+2x^2}+4e^{3y+2x^2}x(x-y))