Calculus #3: d ( sin ⁡ ( 2 x ) ) d x \frac{d(\sin(2x))}{dx}

Calculus Level 2

The derivative of sin ⁡ ( x ) \sin(x) is cos ⁡ ( x ) \cos(x) .

Fill in the blank:

Therefore the derivative of sin ⁡ ( 2 x ) \sin(2x) with respect to x x is _ .

See more calculus problems .

2 × sin ⁡ ( 2 x ) 2 \times \sin(2x) 2 × cos ⁡ ( 2 x ) 2 \times \cos(2x) cos ⁡ ( 2 x ) \cos(2x) cos ⁡ ( 2 ) × sin ⁡ ( 2 x ) \cos(2) \times \sin(2x) 2 × cos ⁡ ( x ) 2 \times \cos(x) c o s ( 2 ) × cos ⁡ ( 2 x ) cos(2) \times \cos(2x) sin ⁡ ( 2 x ) \sin(2x) 2 × sin ⁡ ( x ) 2 \times \sin(x)

Ron Lauterbach by Ron Lauterbach , 18, Germany

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1 solution

Ananth Jayadev
Nov 22, 2017

We are asked to find the derivative of the expression s i n ( 2 x ) sin(2x) ,

In order to solve this we use the Chain Rule:

d ( s i n ( 2 x ) ) d x = c o s ( 2 x ) × 2 = 2 × c o s ( 2 x ) \frac { d(sin(2x)) }{ dx } = cos(2x) \times 2 = 2 \times cos(2x)

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