What is the derivative of 2cos(x+2xsin(x)) ?

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

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

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

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

2 x cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

= 2 x cos (x)

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

\int (4 x + 5) d x

\frac{d}{d x} (arcsin (\frac{1}{x ^{5}}))

(1 - e^{z}) (z + e^{z})

y^{^{'}} = \frac{( y ^{2} + x ^{2} )}{2 x y}

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