What is (\partial)/(\partial y)(e^{xy}tan(y)) ?

The answer to (\partial)/(\partial y)(e^{xy}tan(y)) is e^{xy}xtan(y)+sec^2(y)e^{xy}

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(\partial)/(\partial y)(e^{xy}tan(y))

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

e^{x y} x tan (y) + sec^{2} (y) e^{x y}

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

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

f = e^{x y}, g = tan (y)

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

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

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

= e^{x y} x tan (y) + sec^{2} (y) e^{x y}

\frac{d}{d x} (1 + \frac{5 e ^{- 2 x^{2}}}{2 - ∣ x ∣})

y = cos (sin (tan (7 x)))

\int_{0}^{8} \frac{1}{( 8 - x )} d x

\int 2 e^{- 0.8 x} d x

x y^{^{'}} + 3 x - 2 y = 0

What is (\partial)/(\partial y)(e^{xy}tan(y)) ?
The answer to (\partial)/(\partial y)(e^{xy}tan(y)) is e^{xy}xtan(y)+sec^2(y)e^{xy}