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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 (e^{x^{2} + y^{2}} \cdot 2 xx + 1 \cdot e^{x^{2} + y^{2}}) : 2 (2 e^{x^{2} + y^{2}} x^{2} + e^{x^{2} + y^{2}})

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

\int \frac{2 y}{1 + y ^{2}} d y

\int tanh (2 x) ln (cosh (2 x)) d x

cos (x), x^{2} + 2, [1, 2]

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

\frac{s}{s ^{2} + s}

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