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

$$( 4 + 2 n ^ { 3 } ) + ( 5 n ^ { 3 } + 2 )$$

Evaluate

$$7n^{3}+6$$

Solution Steps

Combine 2n^{3} and 5n^{3} to get 7n^{3}.

$$4+7n^{3}+2$$

Add 4 and 2 to get 6.

$$6+7n^{3}$$

Differentiate w.r.t. n

$$21n^{2}$$

Steps Using Derivative Rule for Sum

Combine 2n^{3} and 5n^{3} to get 7n^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(4+7n^{3}+2)$$

Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}n}(6+7n^{3})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3\times 7n^{3-1}$$

Multiply 3 times 7.

$$21n^{3-1}$$

Subtract 1 from 3.

$$21n^{2}$$