Solve 3*3*3*3*q*q*q

$$3 \times 3 \times 3 \times 3 \times q \times q \times q$$

Evaluate

$$81q^{3}$$

Solution Steps

Multiply q and q to get q^{2}.

$$3\times 3\times 3\times 3q^{2}q$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$3\times 3\times 3\times 3q^{3}$$

Multiply 3 and 3 to get 9.

$$9\times 3\times 3q^{3}$$

Multiply 9 and 3 to get 27.

$$27\times 3q^{3}$$

Multiply 27 and 3 to get 81.

$$81q^{3}$$

Differentiate w.r.t. q

$$243q^{2}$$

Steps Using Definition of a Derivative

Multiply q and q to get q^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}q}(9\times 3\times 3q^{3})$$

Multiply 9 and 3 to get 27.

$$\frac{\mathrm{d}}{\mathrm{d}q}(27\times 3q^{3})$$

Multiply 27 and 3 to get 81.

$$\frac{\mathrm{d}}{\mathrm{d}q}(81q^{3})$$

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

$$3\times 81q^{3-1}$$

Multiply 3 times 81.

$$243q^{3-1}$$

Subtract 1 from 3.

$$243q^{2}$$