Solve 3a^2b/5c^2:-9ab/c^2=

$$\frac { 3 a ^ { 2 } b } { 5 c ^ { 2 } } : \frac { - 9 a b } { c ^ { 2 } } =$$

Evaluate

$$-\frac{a}{15}$$

Solution Steps

Divide \frac{3a^{2}b}{5c^{2}} by \frac{-9ab}{c^{2}} by multiplying \frac{3a^{2}b}{5c^{2}} by the reciprocal of \frac{-9ab}{c^{2}}.

$$\frac{3a^{2}bc^{2}}{5c^{2}\left(-9\right)ab}$$

Cancel out 3abc^{2} in both numerator and denominator.

$$\frac{a}{-3\times 5}$$

Multiply -3 and 5 to get -15.

$$\frac{a}{-15}$$

Differentiate w.r.t. a

$$-\frac{1}{15} = -0.06666666666666667$$

Steps Using Definition of a Derivative

Divide \frac{3a^{2}b}{5c^{2}} by \frac{-9ab}{c^{2}} by multiplying \frac{3a^{2}b}{5c^{2}} by the reciprocal of \frac{-9ab}{c^{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3a^{2}bc^{2}}{5c^{2}\left(-9\right)ab})$$

Cancel out 3abc^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a}{-3\times 5})$$

Multiply -3 and 5 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a}{-15})$$

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

$$-\frac{1}{15}a^{1-1}$$

Subtract 1 from 1.

$$-\frac{1}{15}a^{0}$$

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

$$-\frac{1}{15}$$