What is (\partial)/(\partial x)(x^2e^{5xy}) ?

The answer to (\partial)/(\partial x)(x^2e^{5xy}) is 2xe^{5xy}+e^{5xy}*5yx^2

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(\partial)/(\partial x)(x^2e^{5xy})

\frac{\partial}{\partial x} (x^{2} e^{5 x y})

2 x e^{5 x y} + e^{5 x y} \cdot 5 y x^{2}

Solution steps

\frac{\partial}{\partial x} (x^{2} e^{5 x y})

Treat

y

as a constant

Apply the Product Rule:

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

f = x^{2}, g = e^{5 x y}

= \frac{\partial}{\partial x} (x^{2}) e^{5 x y} + \frac{\partial}{\partial x} (e^{5 x y}) x^{2}

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

\frac{\partial}{\partial x} (e^{5 x y}) = e^{5 x y} \cdot 5 y

= 2 x e^{5 x y} + e^{5 x y} \cdot 5 y x^{2}

\frac{d}{d x} (- ln (1 + 6 x))

\frac{\partial}{\partial x} (cos^{n} (x))

\int_{0.5}^{1} \frac{4}{9} x (5 - x^{2}) d x

x \to 0 - lim (- 2 x^{2} + 2 x)

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

What is (\partial)/(\partial x)(x^2e^{5xy}) ?
The answer to (\partial)/(\partial x)(x^2e^{5xy}) is 2xe^{5xy}+e^{5xy}*5yx^2