What is (\partial)/(\partial x)(x^{2y}+4y) ?

The answer to (\partial)/(\partial x)(x^{2y}+4y) is 2yx^{2y-1}

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(\partial)/(\partial x)(x^{2y}+4y)

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

2 y x^{2 y - 1}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (4 y) = 0

= 2 y x^{2 y - 1} + 0

Simplify

= 2 y x^{2 y - 1}

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

\frac{d}{d x} (ln (\frac{x + 2}{x - 2}))

y = 6 x^{4} ln (x)

f (x) = 5 x, at x = 5

\int tan (5 x) sec^{2} (5 x) d x

What is (\partial)/(\partial x)(x^{2y}+4y) ?
The answer to (\partial)/(\partial x)(x^{2y}+4y) is 2yx^{2y-1}