Solve (4n-3n^3)+(3n^3+4n)

$$( 4 n - 3 n ^ { 3 } ) + ( 3 n ^ { 3 } + 4 n )$$

Evaluate

$$8n$$

Solution Steps

Combine -3n^{3} and 3n^{3} to get 0.

$$4n+4n$$

Combine 4n and 4n to get 8n.

$$8n$$

Differentiate w.r.t. n

$$8$$

Steps Using Definition of a Derivative

Combine -3n^{3} and 3n^{3} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}n}(4n+4n)$$

Combine 4n and 4n to get 8n.

$$\frac{\mathrm{d}}{\mathrm{d}n}(8n)$$

The derivative of ax^{n} is nax^{n-1}.

$$8n^{1-1}$$

Subtract 1 from 1.

$$8n^{0}$$

For any term t except 0, t^{0}=1.

$$8\times 1$$

For any term t, t\times 1=t and 1t=t.

$$8$$