What is the derivative of sin(x(-2x)) ?

The derivative of sin(x(-2x)) is -2xcos(x)-2sin(x)

What is the first derivative of sin(x(-2x)) ?

The first derivative of sin(x(-2x)) is -2xcos(x)-2sin(x)

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

What is the derivative of sin(x(-2x)) ?
The derivative of sin(x(-2x)) is -2xcos(x)-2sin(x)
What is the first derivative of sin(x(-2x)) ?
The first derivative of sin(x(-2x)) is -2xcos(x)-2sin(x)