What is (\partial)/(\partial y)(e^{3x}*tan(y)) ?

The answer to (\partial)/(\partial y)(e^{3x}*tan(y)) is e^{3x}sec^2(y)

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(\partial)/(\partial y)(e^{3x}*tan(y))

\frac{\partial}{\partial y} (e^{3 x} \cdot tan (y))

e^{3 x} sec^{2} (y)

Solution steps

\frac{\partial}{\partial y} (e^{3 x} tan (y))

Treat

x

as a constant

Take the constant out:

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

= e^{3 x} \frac{\partial}{\partial y} (tan (y))

Apply the common derivative:

\frac{\partial}{\partial y} (tan (y)) = sec^{2} (y)

= e^{3 x} sec^{2} (y)

What is (\partial)/(\partial y)(e^{3x}*tan(y)) ?
The answer to (\partial)/(\partial y)(e^{3x}*tan(y)) is e^{3x}sec^2(y)