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

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

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

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

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

- cos (2 x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= - cos (2 x)

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