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

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

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

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

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\frac{d}{d x} (3 sin (2 x) cos (x))

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

Solution steps

\frac{d}{d x} (3 sin (2 x) cos (x))

Take the constant out:

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

= 3 \frac{d}{d x} (sin (2 x) cos (x))

Apply the Product Rule:

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

f = sin (2 x), g = cos (x)

= 3 (\frac{d}{d x} (sin (2 x)) cos (x) + \frac{d}{d x} (cos (x)) sin (2 x))

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

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

= 3 (cos (2 x) \cdot 2 cos (x) + (- sin (x)) sin (2 x))

Simplify

= 3 (2 cos (2 x) cos (x) - sin (x) sin (2 x))

\frac{\partial}{\partial t} (1)

f (x) = \frac{x ^{2} + 2 x + 3}{x ^{2} + 2 x + 1}

\frac{\partial}{\partial x} (- yz)

y = cos (sin (tan (5 x)))

3^{x^{2} + 1}

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