What is the derivative of 4cos(xsin(x)) ?

The derivative of 4cos(xsin(x)) is 4cos(2x)

What is the first derivative of 4cos(xsin(x)) ?

The first derivative of 4cos(xsin(x)) is 4cos(2x)

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

4 cos (2 x)

Solution steps

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

Simplify

4 cos (x) sin (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)

f (x) = \frac{x ^{3} + 9}{x ^{3}}

\frac{d}{d x} (\frac{x ^{2} + 3 x}{7})

\frac{d}{d s} (\frac{s}{s ^{2} + 4})

e^{3 x} (3 cos (4 x) - 4 sin (4 x))

\int \frac{- 5 x ^{2}}{4 x - x ^{2}} d x

What is the derivative of 4cos(xsin(x)) ?
The derivative of 4cos(xsin(x)) is 4cos(2x)
What is the first derivative of 4cos(xsin(x)) ?
The first derivative of 4cos(xsin(x)) is 4cos(2x)