What is (\partial)/(\partial x)(2y+3ysin(x)) ?

The answer to (\partial)/(\partial x)(2y+3ysin(x)) is 3ycos(x)

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(\partial)/(\partial x)(2y+3ysin(x))

\frac{\partial}{\partial x} (2 y + 3 y sin (x))

3 y cos (x)

Solution steps

\frac{\partial}{\partial x} (2 y + 3 y sin (x))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 y) + \frac{\partial}{\partial x} (3 y sin (x))

\frac{\partial}{\partial x} (2 y) = 0

\frac{\partial}{\partial x} (3 y sin (x)) = 3 y cos (x)

= 0 + 3 y cos (x)

Simplify

= 3 y cos (x)

\frac{d}{d x} (arcsin (\frac{x}{1 + x ^{2}}))

\int \frac{z ^{4} + 10 z ^{2} + 25}{z ^{3} + 5 z} d z

n = 1 \sum \infty (1 + \frac{1}{n})^{n}

\frac{d}{d x} (x (4 - x)^{3})

\int \frac{1}{2 + t} d t

What is (\partial)/(\partial x)(2y+3ysin(x)) ?
The answer to (\partial)/(\partial x)(2y+3ysin(x)) is 3ycos(x)