What is (\partial)/(\partial x)(2e^{4xy}) ?

The answer to (\partial)/(\partial x)(2e^{4xy}) is 8e^{4xy}y

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(\partial)/(\partial x)(2e^{4xy})

\frac{\partial}{\partial x} (2 e^{4 x y})

8 e^{4 x y} y

Solution steps

\frac{\partial}{\partial x} (2 e^{4 x y})

Treat

y

as a constant

Take the constant out:

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

= 2 \frac{\partial}{\partial x} (e^{4 x y})

Apply the chain rule:

e^{4 x y} \frac{\partial}{\partial x} (4 x y)

= e^{4 x y} \frac{\partial}{\partial x} (4 x y)

\frac{\partial}{\partial x} (4 x y) = 4 y

= 2 e^{4 x y} \cdot 4 y

Simplify

= 8 e^{4 x y} y

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

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f (x) = x^{2} - x, at x = - 2

\int_{0}^{0.5} (- 13 x + 6) - (- x) d x

What is (\partial)/(\partial x)(2e^{4xy}) ?
The answer to (\partial)/(\partial x)(2e^{4xy}) is 8e^{4xy}y