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Popular >

derivative of 2sin(x)+2xcos(x)

Solution

derivative of

2 sin (x) + 2 x cos (x)

Solution

4 cos (x) - 2 x sin (x)

Solution steps

\frac{d}{d x} (2 sin (x) + 2 x cos (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 sin (x)) + \frac{d}{d x} (2 x cos (x))

\frac{d}{d x} (2 sin (x)) = 2 cos (x)

\frac{d}{d x} (2 x cos (x)) = 2 (cos (x) - x sin (x))

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

Simplify

2 cos (x) + 2 (cos (x) - x sin (x)) : 4 cos (x) - 2 x sin (x)

= 4 cos (x) - 2 x sin (x)

Popular Examples

integral of e^ycos(2y)

\int e^{y} cos (2 y) d y

limit as x approaches 2 of (2x-25)/(x-2)

x \to 2 lim (\frac{2 x - 25}{x - 2})

implicit (dy)/(dx),xy=y^2 implicit derivative

\frac{d y}{d x}, x y = y^{2}

integral from-infinity to 0 of 1/(6-10x)

\int_{- \infty}^{0} \frac{1}{6 - 10 x} d x

area |9x|,x^2-10 area

∣ 9 x ∣, x^{2} - 10

Frequently Asked Questions (FAQ)

What is the derivative of 2sin(x)+2xcos(x) ?
The derivative of 2sin(x)+2xcos(x) is 4cos(x)-2xsin(x)
What is the first derivative of 2sin(x)+2xcos(x) ?
The first derivative of 2sin(x)+2xcos(x) is 4cos(x)-2xsin(x)