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)

\int sec^{10} (x) d x

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

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

f (t) = - 16 t^{2} + 32 t + 240, at t = 0

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

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