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{2}{5} x d x

2 + x^{2}

n = 0 \sum \infty 2 (- \frac{2}{3})^{n}

\frac{1}{3} x^{3} - 3 x^{2} - 16 x + 8

y^{^{'}} cot^{2} (x) + tan (y) = 0

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)