Solve 2(3n)+5(5n)+4(4n)

$$2 ( 3 n ) + 5 ( 5 n ) + 4 ( 4 n )$$

Evaluate

$$47n$$

Solution Steps

Multiply 2 and 3 to get 6. Multiply 5 and 5 to get 25. Multiply 4 and 4 to get 16.

$$6n+25n+16n$$

Combine 6n and 25n to get 31n.

$$31n+16n$$

Combine 31n and 16n to get 47n.

$$47n$$

Differentiate w.r.t. n

$$47$$

Steps Using Definition of a Derivative

Multiply 2 and 3 to get 6. Multiply 5 and 5 to get 25. Multiply 4 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}n}(6n+25n+16n)$$

Combine 6n and 25n to get 31n.

$$\frac{\mathrm{d}}{\mathrm{d}n}(31n+16n)$$

Combine 31n and 16n to get 47n.

$$\frac{\mathrm{d}}{\mathrm{d}n}(47n)$$

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

$$47n^{1-1}$$

Subtract 1 from 1.

$$47n^{0}$$

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

$$47\times 1$$

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

$$47$$