What is (\partial)/(\partial x)(xsin(x)) ?

The answer to (\partial)/(\partial x)(xsin(x)) is sin(x)+xcos(x)

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(\partial)/(\partial x)(xsin(x))

\frac{\partial}{\partial x} (x sin (x))

sin (x) + x cos (x)

Solution steps

\frac{\partial}{\partial x} (x sin (x))

Apply the Product Rule:

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

f = x, g = sin (x)

= \frac{\partial}{\partial x} (x) sin (x) + \frac{\partial}{\partial x} (sin (x)) x

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

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

= 1 \cdot sin (x) + cos (x) x

Simplify

= sin (x) + x cos (x)

\frac{\partial}{\partial x} (y^{x^{7}})

x \to + 2 lim (\frac{x ^{2} - 4}{x - 2})

a re a x^{2}, 4 x

a re a y = 1 + 2 x, y = \frac{3 + x}{3}

a re a x, \frac{x}{2}

What is (\partial)/(\partial x)(xsin(x)) ?
The answer to (\partial)/(\partial x)(xsin(x)) is sin(x)+xcos(x)