What is (\partial)/(\partial x)(sin(x)+xcos(x)) ?

The answer to (\partial)/(\partial x)(sin(x)+xcos(x)) is 2cos(x)-xsin(x)

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(\partial)/(\partial x)(sin(x)+xcos(x))

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

2 cos (x) - x sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= cos (x) + cos (x) - x sin (x)

Simplify

= 2 cos (x) - x sin (x)

\frac{d y}{d t} = 4 - \frac{1.5 y}{10 + 2.5 t}

\int 6 tan^{4} (x) d x

\frac{\partial}{\partial x} (2 x + y + 1)

\int \frac{3 x ^{2} - 7}{x ^{3} - 7 x + 6} d x

\int_{0}^{1} (t 4 + 9 t^{2}) d t

What is (\partial)/(\partial x)(sin(x)+xcos(x)) ?
The answer to (\partial)/(\partial x)(sin(x)+xcos(x)) is 2cos(x)-xsin(x)