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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

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

e^{- 5 x} + e^{2 x}

x \to - 2 lim (x^{2} - x)

\frac{d}{d x} (x \cdot sin (x) + cos (x))

\frac{20}{s ^{2} + 10}

\int_{0}^{1} \frac{1}{1 + t ^{2}} d t

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