What is the derivative of-4sin(xcos(x)) ?

The derivative of-4sin(xcos(x)) is -4cos(2x)

What is the first derivative of-4sin(xcos(x)) ?

The first derivative of-4sin(xcos(x)) is -4cos(2x)

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\frac{d}{d x} (- 4 sin (x) cos (x))

- 4 cos (2 x)

Solution steps

\frac{d}{d x} (- 4 sin (x) cos (x))

Simplify

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

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

Take the constant out:

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

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

Apply the chain rule:

cos (2 x) \frac{d}{d x} (2 x)

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

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

= - 2 cos (2 x) \cdot 2

Simplify

= - 4 cos (2 x)

\int \frac{3}{x + 4} d x

f (x) = x^{3} + x, at x = 2

cos (sin^{2} (x - 2))

x \to 0 + lim (arctan (ln (0)))

\frac{\partial}{\partial x} (4 x^{2} y^{3} + 1)

What is the derivative of-4sin(xcos(x)) ?
The derivative of-4sin(xcos(x)) is -4cos(2x)
What is the first derivative of-4sin(xcos(x)) ?
The first derivative of-4sin(xcos(x)) is -4cos(2x)