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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

derivative of f(x)=(e^x)/(1+e^x)derivative of

f (x) = \frac{e ^{x}}{1 + e ^{x}}

integral of (x^2)/((16-x^3)^2)

\int \frac{x ^{2}}{( 16 - x ^{3} ) ^{2}} d x

limit as x approaches-4+of (x+3)/(x+4)

x \to - 4 + lim (\frac{x + 3}{x + 4})

integral of x^2sec^2(x)tan(x)

\int x^{2} sec^{2} (x) tan (x) d x

area y=x^2-4,y=2-5x^2 area

y = x^{2} - 4, y = 2 - 5 x^{2}

Frequently Asked Questions (FAQ)

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