What is (\partial)/(\partial y)(2(y+1)e^{2x}) ?

The answer to (\partial)/(\partial y)(2(y+1)e^{2x}) is 2e^{2x}

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(\partial)/(\partial y)(2(y+1)e^{2x})

\frac{\partial}{\partial y} (2 (y + 1) e^{2 x})

2 e^{2 x}

Solution steps

\frac{\partial}{\partial y} (2 (y + 1) e^{2 x})

Treat

x

as a constant

Take the constant out:

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

= 2 e^{2 x} \frac{\partial}{\partial y} (y + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 2 e^{2 x} (\frac{\partial}{\partial y} (y) + \frac{\partial}{\partial y} (1))

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

\frac{\partial}{\partial y} (1) = 0

= 2 e^{2 x} (1 + 0)

Simplify

= 2 e^{2 x}

(- 6, 3), (4, - 1)

- 19.6 x + 2

\int \frac{1}{x + 1} d x

\frac{\partial}{\partial y} (x^{2} - 4 x y + y^{3} + 4 y)

What is (\partial)/(\partial y)(2(y+1)e^{2x}) ?
The answer to (\partial)/(\partial y)(2(y+1)e^{2x}) is 2e^{2x}