Solve q^3+q^3+q^3+q^3

$$q ^ { 3 } + q ^ { 3 } + q ^ { 3 } + q ^ { 3 }$$

Evaluate

$$4q^{3}$$

Solution Steps

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

$$2q^{3}+q^{3}+q^{3}$$

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

$$3q^{3}+q^{3}$$

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

$$4q^{3}$$

Differentiate w.r.t. q

$$12q^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}q}(2q^{3}+q^{3}+q^{3})$$

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}q}(4q^{3})$$

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

$$3\times 4q^{3-1}$$

Multiply 3 times 4.

$$12q^{3-1}$$

Subtract 1 from 3.

$$12q^{2}$$