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

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

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(\partial)/(\partial x)(x^2+2ysin(x))

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

2 x + 2 y cos (x)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

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

= 2 x + 2 y cos (x)

x \to 0.9 lim (4 x)

(1 + x^{2}) d y - (1 + 4 y^{2}) d x = 0

\int (x^{2} + 6) \cdot e^{(- x)} d x

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

n = 1 \sum \infty \frac{( 1 )}{2 n + 1}

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