What is expand 30(1/3 sin(3x)-1/2 cos(2x)+1/5 e^{5x}) ?

The solution to expand 30(1/3 sin(3x)-1/2 cos(2x)+1/5 e^{5x}) is 10sin(3x)-15cos(2x)+6e^{5x}

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expand 30(1/3 sin(3x)-1/2 cos(2x)+1/5 e^{5x})

expand

30 (\frac{1}{3} sin (3 x) - \frac{1}{2} cos (2 x) + \frac{1}{5} e^{5 x})

10 sin (3 x) - 15 cos (2 x) + 6 e^{5 x}

Solution steps

30 (\frac{1}{3} sin (3 x) - \frac{1}{2} cos (2 x) + \frac{1}{5} e^{5 x})

Distribute parentheses

= 30 \cdot \frac{1}{3} sin (3 x) + 30 (- \frac{1}{2} cos (2 x)) + 30 \cdot \frac{1}{5} e^{5 x}

Apply minus-plus rules

+ (- a) = - a

= 30 \cdot \frac{1}{3} sin (3 x) - 30 \cdot \frac{1}{2} cos (2 x) + 30 \cdot \frac{1}{5} e^{5 x}

Simplify

30 \cdot \frac{1}{3} sin (3 x) - 30 \cdot \frac{1}{2} cos (2 x) + 30 \cdot \frac{1}{5} e^{5 x} : 10 sin (3 x) - 15 cos (2 x) + 6 e^{5 x}

= 10 sin (3 x) - 15 cos (2 x) + 6 e^{5 x}

\frac{d}{d y} ((x) (- 5 x^{2} + 20 x + 2))

2^{4}

\frac{2 ( - 8 x ^{3} + 72 x ^{2} - 216 x + 216 )}{27}

x e^{x} (x e^{x} - 1)

What is expand 30(1/3 sin(3x)-1/2 cos(2x)+1/5 e^{5x}) ?
The solution to expand 30(1/3 sin(3x)-1/2 cos(2x)+1/5 e^{5x}) is 10sin(3x)-15cos(2x)+6e^{5x}