Solve 14p^4/9^6*q^5/56p^4=

$$\frac { 14 p ^ { 4 } } { 9 ^ { 6 } } \cdot \frac { q ^ { 5 } } { 56 p ^ { 4 } } =$$

Evaluate

$$\frac{q^{5}}{2125764}$$

Solution Steps

Calculate 9 to the power of 6 and get 531441.

$$\frac{14p^{4}}{531441}\times \frac{q^{5}}{56p^{4}}$$

Multiply \frac{14p^{4}}{531441} times \frac{q^{5}}{56p^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14p^{4}q^{5}}{531441\times 56p^{4}}$$

Cancel out 14p^{4} in both numerator and denominator.

$$\frac{q^{5}}{4\times 531441}$$

Multiply 4 and 531441 to get 2125764.

$$\frac{q^{5}}{2125764}$$

Differentiate w.r.t. q

$$\frac{5q^{4}}{2125764}$$

Steps Using Definition of a Derivative

Calculate 9 to the power of 6 and get 531441.

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{14p^{4}}{531441}\times \frac{q^{5}}{56p^{4}})$$

Multiply \frac{14p^{4}}{531441} times \frac{q^{5}}{56p^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{14p^{4}q^{5}}{531441\times 56p^{4}})$$

Cancel out 14p^{4} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{q^{5}}{4\times 531441})$$

Multiply 4 and 531441 to get 2125764.

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{q^{5}}{2125764})$$

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

$$5\times \frac{1}{2125764}q^{5-1}$$

Multiply 5 times \frac{1}{2125764}.

$$\frac{5}{2125764}q^{5-1}$$

Subtract 1 from 5.

$$\frac{5}{2125764}q^{4}$$