What is the derivative of 3sin(xcos(x)) ?

The derivative of 3sin(xcos(x)) is 3cos(2x)

What is the first derivative of 3sin(xcos(x)) ?

The first derivative of 3sin(xcos(x)) is 3cos(2x)

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\frac{d}{d x} (3 sin (x) cos (x))

3 cos (2 x)

Solution steps

\frac{d}{d x} (3 sin (x) cos (x))

Take the constant out:

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

= 3 \frac{d}{d x} (sin (x) cos (x))

Apply the Product Rule:

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

f = sin (x), g = cos (x)

= 3 (\frac{d}{d x} (sin (x)) cos (x) + \frac{d}{d x} (cos (x)) sin (x))

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

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

= 3 (cos (x) cos (x) + (- sin (x)) sin (x))

Simplify

3 (cos (x) cos (x) + (- sin (x)) sin (x)) : 3 cos (2 x)

= 3 cos (2 x)

f (x) = x^{- 1} - \frac{1}{x}

x \to 2 lim (x)

\frac{d}{d x} (\frac{2}{3 x - 1})

\int y^{2} cos (x) + z^{3} d x

f^{^{''}} (x) = 4 x^{2} + 8 x - 17

What is the derivative of 3sin(xcos(x)) ?
The derivative of 3sin(xcos(x)) is 3cos(2x)
What is the first derivative of 3sin(xcos(x)) ?
The first derivative of 3sin(xcos(x)) is 3cos(2x)