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

The answer to (\partial)/(\partial x)(bxe^{5xy}) is b(e^{5xy}+5e^{5xy}xy)

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(\partial)/(\partial x)(bxe^{5xy})

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

b (e^{5 x y} + 5 e^{5 x y} x y)

Solution steps

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

Treat

b, y

as constants

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

= b (1 \cdot e^{5 x y} + e^{5 x y} \cdot 5 y x)

Simplify

= b (e^{5 x y} + 5 e^{5 x y} x y)

x \to (- 1) + lim (\frac{1}{x + 1})

x \to 2 lim (\frac{\frac{4}{x} - 2}{x - 2})

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

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

f (x) = e^{6} + ln (4)

What is (\partial)/(\partial x)(bxe^{5xy}) ?
The answer to (\partial)/(\partial x)(bxe^{5xy}) is b(e^{5xy}+5e^{5xy}xy)