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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derivative of

x \cdot 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)

\int 6 (36 - 4 x)^{\frac{1}{2}} d x

\int \frac{x ^{3}}{( x ^{2} - 16 )} d x

y = x, y = - x, x = 1

\int x (x + 6)^{5} d x

\int e^{s i n (2 x)} cos (2 x) d 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)