Solve (7+2q^3)+(4q^3-8)

$$( 7 + 2 q ^ { 3 } ) + ( 4 q ^ { 3 } - 8 )$$

Evaluate

$$6q^{3}-1$$

Solution Steps

Combine 2q^{3} and 4q^{3} to get 6q^{3}.

$$7+6q^{3}-8$$

Subtract 8 from 7 to get -1.

$$-1+6q^{3}$$

Differentiate w.r.t. q

$$18q^{2}$$

Steps Using Derivative Rule for Sum

Combine 2q^{3} and 4q^{3} to get 6q^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}q}(7+6q^{3}-8)$$

Subtract 8 from 7 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}q}(-1+6q^{3})$$

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}.

$$3\times 6q^{3-1}$$

Multiply 3 times 6.

$$18q^{3-1}$$

Subtract 1 from 3.

$$18q^{2}$$