What is the derivative of sin(x)+xcos(x) ?

The derivative of sin(x)+xcos(x) is 2cos(x)-xsin(x)

What is the first derivative of sin(x)+xcos(x) ?

The first derivative of sin(x)+xcos(x) is 2cos(x)-xsin(x)

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derivative of

sin (x) + x cos (x)

2 cos (x) - x sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d 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}{d x} (6^{x^{2}})

\frac{d}{d x} (\frac{( 6 x ^{2} + 8 x + 2 )}{x})

\frac{\partial}{\partial x} (30 y^{4} sin (2 x))

(x - 4) ln (4 - x)

\frac{d}{d x} (x sin (4 x))

What is the derivative of sin(x)+xcos(x) ?
The derivative of sin(x)+xcos(x) is 2cos(x)-xsin(x)
What is the first derivative of sin(x)+xcos(x) ?
The first derivative of sin(x)+xcos(x) is 2cos(x)-xsin(x)