Solve q^2*q^3divq^4

$$q ^ { 2 } \times q ^ { 3 } \div q ^ { 4 }$$

Evaluate

$$q$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{q^{5}}{q^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$q^{1}$$

Calculate q to the power of 1 and get q.

$$q$$

Differentiate w.r.t. q

$$1$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{q^{5}}{q^{4}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}q}(q^{1})$$

Calculate q to the power of 1 and get q.

$$\frac{\mathrm{d}}{\mathrm{d}q}(q)$$

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

$$q^{1-1}$$

Subtract 1 from 1.

$$q^{0}$$

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

$$1$$