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

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

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

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

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

sin (3) (2 x cos (2 x) - 2 x^{2} sin (2 x))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{2}, g = cos (2 x)

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

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

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

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

Simplify

= sin (3) (2 x cos (2 x) - 2 x^{2} sin (2 x))

\int t \cdot e^{t} d t

y^{^{''}} - y^{^{'}} + 121 y = 11 sin (11 t)

\int \frac{1}{x x - 2} d x

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{2 x}

\int \frac{1}{x + 1} d x

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