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Popular >

derivative of cos(2xsin(2x))

Solution

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

Solution

2 cos (4 x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (2 x), g = sin (2 x)

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

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

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

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

Simplify

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

= 2 cos (4 x)

Popular Examples

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\int \frac{sin ( 0 ) d ^{0}}{4 + cos ^{2} ( 0 )} dd

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\frac{5}{s ( s ^{2} + s + 2 )}

(dy)/(dx)y=13^x+e^2

\frac{d y}{d x} y = 1 3^{x} + e^{2}

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\int_{- \frac{π}{6}}^{0} 4 sec^{3} (x) d x

limit as h approaches 0 of (e^h-1)/h

h \to 0 lim (\frac{e ^{h} - 1}{h})

Frequently Asked Questions (FAQ)

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