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{4}{x}, at x = \frac{1}{9}

\frac{d}{d x} (\frac{x ^{3}}{3} - x^{2} - 15 x)

x \to 1 lim (\frac{x ^{2} + 3}{x - 1})

\int_{2}^{3} x^{3} d x

\frac{d}{d x} (\frac{1}{7 x ^{\frac{6}{7}}})

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)