f(x)=x^4sin(2x)+5x^3cos(3x)-4xsin(2x)+8cos(3x)

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Solution for f(x)=x^4sin(2x)+5x^3cos(3x)-4xsin(2x)+8cos(3x) equation: 


Simplifying
f(x) = x4sin(2x) + 5x3cos(3x) + -4xsin(2x) + 8cos(3x)

Multiply f * x
fx = x4sin(2x) + 5x3cos(3x) + -4xsin(2x) + 8cos(3x)

Remove parenthesis around (2x)
fx = insx4 * 2x + 5x3cos(3x) + -4xsin(2x) + 8cos(3x)

Reorder the terms for easier multiplication:
fx = 2insx4 * x + 5x3cos(3x) + -4xsin(2x) + 8cos(3x)

Multiply insx4 * x
fx = 2insx5 + 5x3cos(3x) + -4xsin(2x) + 8cos(3x)

Remove parenthesis around (3x)
fx = 2insx5 + 5cosx3 * 3x + -4xsin(2x) + 8cos(3x)

Reorder the terms for easier multiplication:
fx = 2insx5 + 5 * 3cosx3 * x + -4xsin(2x) + 8cos(3x)

Multiply 5 * 3
fx = 2insx5 + 15cosx3 * x + -4xsin(2x) + 8cos(3x)

Multiply cosx3 * x
fx = 2insx5 + 15cosx4 + -4xsin(2x) + 8cos(3x)

Remove parenthesis around (2x)
fx = 2insx5 + 15cosx4 + -4insx * 2x + 8cos(3x)

Reorder the terms for easier multiplication:
fx = 2insx5 + 15cosx4 + -4 * 2insx * x + 8cos(3x)

Multiply -4 * 2
fx = 2insx5 + 15cosx4 + -8insx * x + 8cos(3x)

Multiply insx * x
fx = 2insx5 + 15cosx4 + -8insx2 + 8cos(3x)

Remove parenthesis around (3x)
fx = 2insx5 + 15cosx4 + -8insx2 + 8cos * 3x

Reorder the terms for easier multiplication:
fx = 2insx5 + 15cosx4 + -8insx2 + 8 * 3cos * x

Multiply 8 * 3
fx = 2insx5 + 15cosx4 + -8insx2 + 24cos * x

Multiply cos * x
fx = 2insx5 + 15cosx4 + -8insx2 + 24cosx

Reorder the terms:
fx = 24cosx + 15cosx4 + -8insx2 + 2insx5

Solving
fx = 24cosx + 15cosx4 + -8insx2 + 2insx5

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by 'x'.
f = 24cos + 15cosx3 + -8insx + 2insx4

Simplifying
f = 24cos + 15cosx3 + -8insx + 2insx4

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