Solve (q^3r^2)/(qr)^2

$$\frac { ( q ^ { 3 } r ^ { 2 } ) } { ( q r ) ^ { 2 } }$$

Evaluate

$$q$$

Solution Steps

Expand \left(qr\right)^{2}.

$$\frac{q^{3}r^{2}}{q^{2}r^{2}}$$

Cancel out q^{2}r^{2} in both numerator and denominator.

$$q$$

Differentiate w.r.t. q

$$1$$

Steps Using Definition of a Derivative

Expand \left(qr\right)^{2}.

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

Cancel out q^{2}r^{2} in both numerator and denominator.

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

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.

$$1$$