What is (\partial)/(\partial x)(e^{7xy}ln(4y)) ?

The answer to (\partial)/(\partial x)(e^{7xy}ln(4y)) is ln(4y)e^{7xy}*7y

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(\partial)/(\partial x)(e^{7xy}ln(4y))

\frac{\partial}{\partial x} (e^{7 x y} ln (4 y))

ln (4 y) e^{7 x y} \cdot 7 y

Solution steps

\frac{\partial}{\partial x} (e^{7 x y} ln (4 y))

Treat

y

as a constant

Take the constant out:

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

= ln (4 y) \frac{\partial}{\partial x} (e^{7 x y})

Apply the chain rule:

e^{7 x y} \frac{\partial}{\partial x} (7 x y)

= e^{7 x y} \frac{\partial}{\partial x} (7 x y)

\frac{\partial}{\partial x} (7 x y) = 7 y

= ln (4 y) e^{7 x y} \cdot 7 y

What is (\partial)/(\partial x)(e^{7xy}ln(4y)) ?
The answer to (\partial)/(\partial x)(e^{7xy}ln(4y)) is ln(4y)e^{7xy}*7y