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

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

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

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

4 (4 e^{4 x y} x y + e^{4 x y})

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = e^{4 x y}, g = x

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

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

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

= 4 (e^{4 x y} \cdot 4 y x + 1 \cdot e^{4 x y})

Simplify

= 4 (4 e^{4 x y} x y + e^{4 x y})

\int 4 x sec^{2} (x) d x

\frac{d}{d x} (0.2 x)

\int tan (x) sin (x) d x

\int \frac{( 4 x )}{x ^{2} + 3} d x

x + 2, \frac{1}{x + 1}, x = 2, x = 0

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