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

The answer to (\partial)/(\partial x)(4e^{4xy}) is 16e^{4xy}y

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

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

16 e^{4 x y} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 4 \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

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

Simplify

= 16 e^{4 x y} y

t e^{t}

\frac{d}{d x} (e^{x^{4}} + 7 x)

f (x) = x^{2} + 16, at x = 3

\int \frac{e ^{8 x}}{e ^{8 x} + 6} d x

y \to 1 lim (\frac{2 y ^{2} + 3}{y - 1})

What is (\partial)/(\partial x)(4e^{4xy}) ?
The answer to (\partial)/(\partial x)(4e^{4xy}) is 16e^{4xy}y