Solve x[n] = \delta [n^2] 2n(u[n] - u[n - 2])

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Type your math problem... x[n] = \delta [n^2] 2n(u[n] - u[n - 2])

Question

Function

x^{'} (n) = 12 δ u n^{2}

Evaluate

x (n) = δ n^{2} \times 2 n (u n - u (n - 2))

Simplify

More Steps

Evaluate

δ n^{2} \times 2 n (u n - u (n - 2))

Subtract the terms

More Steps

Simplify

u n - u (n - 2)

Expand the expression

u n - u n + 2 u

The sum of two opposites equals 0

0 + 2 u

Remove 0

2 u

δ n^{2} \times 2 n \times 2 u

Multiply the terms with the same base by adding their exponents

δ n^{2 + 1} \times 2 \times 2 u

Add the numbers

δ n^{3} \times 2 \times 2 u

Multiply the terms

δ n^{3} \times 4 u

Use the commutative property to reorder the terms

4 δ n^{3} u

x (n) = 4 δ n^{3} u

Evaluate

x (n) = 4 δ u n^{3}

Take the derivative of both sides

x^{'} (n) = \frac{d}{d n} (4 δ u n^{3})

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

x^{'} (n) = 4 δ u \times \frac{d}{d n} (n^{3})

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

x^{'} (n) = 4 δ u \times 3 n^{2}

Solution

x^{'} (n) = 12 δ u n^{2}

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