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Popular >

derivative of cos(2x+2xsin(2x))

Solution

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

Solution

4 x cos (2 x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

= 4 x cos (2 x)

Popular Examples

(dx)/(dt)=3x(8-x)

\frac{d x}{d t} = 3 x (8 - x)

derivative of 60x^4-160x^3+120x^2-20

\frac{d}{d x} (60 x^{4} - 160 x^{3} + 120 x^{2} - 20)

derivative of (11x^2-22x+22e^x)

\frac{d}{d x} ((11 x^{2} - 22 x + 22) e^{x})

integral of 3sqrt(4x-7)

\int 3 4 x - 7 d x

(\partial)/(\partial y)(ln(x^2+y^2)-z)

\frac{\partial}{\partial y} (ln (x^{2} + y^{2}) - z)

Frequently Asked Questions (FAQ)

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