What is the derivative of x(cos(x)) ?

The derivative of x(cos(x)) is cos(x)-xsin(x)

What is the first derivative of x(cos(x)) ?

The first derivative of x(cos(x)) is cos(x)-xsin(x)

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

cos (x) - x sin (x)

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot cos (x) + (- sin (x)) x

Simplify

= cos (x) - x sin (x)

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