What is the derivative of 5(2xcos(3x)-3x^2sin(3x)) ?

The derivative of 5(2xcos(3x)-3x^2sin(3x)) is 5(2cos(3x)-12xsin(3x)-9x^2cos(3x))

What is the first derivative of 5(2xcos(3x)-3x^2sin(3x)) ?

The first derivative of 5(2xcos(3x)-3x^2sin(3x)) is 5(2cos(3x)-12xsin(3x)-9x^2cos(3x))

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derivative of

5 (2 x cos (3 x) - 3 x^{2} sin (3 x))

5 (2 cos (3 x) - 12 x sin (3 x) - 9 x^{2} cos (3 x))

Solution steps

\frac{d}{d x} (5 (2 x cos (3 x) - 3 x^{2} sin (3 x)))

Take the constant out:

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

= 5 \frac{d}{d x} (2 x cos (3 x) - 3 x^{2} sin (3 x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 5 (\frac{d}{d x} (2 x cos (3 x)) - \frac{d}{d x} (3 x^{2} sin (3 x)))

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

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

= 5 (2 (cos (3 x) - 3 x sin (3 x)) - 3 (2 x sin (3 x) + cos (3 x) \cdot 3 x^{2}))

Expand

2 (cos (3 x) - 3 x sin (3 x)) - 3 (2 x sin (3 x) + cos (3 x) \cdot 3 x^{2}) : 2 cos (3 x) - 12 x sin (3 x) - 9 x^{2} cos (3 x)

= 5 (2 cos (3 x) - 12 x sin (3 x) - 9 x^{2} cos (3 x))

y^{^{'}} = - \frac{2 y}{x}

\frac{d}{d x} (x^{3} + 3 x + 1)

\frac{\partial}{\partial x} (9 x^{2} - 7)

\int x^{3} \cdot 5^{- x} d x

f (x) = x arcsin (x)

What is the derivative of 5(2xcos(3x)-3x^2sin(3x)) ?
The derivative of 5(2xcos(3x)-3x^2sin(3x)) is 5(2cos(3x)-12xsin(3x)-9x^2cos(3x))
What is the first derivative of 5(2xcos(3x)-3x^2sin(3x)) ?
The first derivative of 5(2xcos(3x)-3x^2sin(3x)) is 5(2cos(3x)-12xsin(3x)-9x^2cos(3x))