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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int \frac{u}{u ^{2} - 1} d u

\frac{d N}{d t} = \frac{t e ^{t}}{N ^{2}}

n = 0 \sum \infty \frac{1}{n ^{5}}

n = 8 \sum \infty (\frac{1}{4})^{n}

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