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

The answer to (\partial)/(\partial x)(e^{3x^2+y}(x-y)) is 6e^{3x^2+y}x(x-y)+e^{3x^2+y}

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

\frac{\partial}{\partial x} (e^{3 x^{2} + y}) = e^{3 x^{2} + y} \cdot 6 x

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

= e^{3 x^{2} + y} \cdot 6 x (x - y) + 1 \cdot e^{3 x^{2} + y}

Simplify

= 6 e^{3 x^{2} + y} x (x - y) + e^{3 x^{2} + y}

y^{^{''}} - 2 y^{^{'}} + y = x e^{x} + 4

\int (x^{2} (x^{3} - 1)^{10}) d x

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

\int \frac{3 x ^{2} + 5 x + 3}{( x ^{2} + 1 ) ^{2}} d x

f (x) = 5 x^{2} tan (1 - x)

What is (\partial)/(\partial x)(e^{3x^2+y}(x-y)) ?
The answer to (\partial)/(\partial x)(e^{3x^2+y}(x-y)) is 6e^{3x^2+y}x(x-y)+e^{3x^2+y}