Solve 4ab^3*-3a/2b^3

$$4 a b ^ { 3 } \times \frac { - 3 a } { 2 b ^ { 3 } }$$

Evaluate

$$-6a^{2}$$

Solution Steps

Express 4\times \frac{-3a}{2b^{3}} as a single fraction.

$$\frac{4\left(-3\right)a}{2b^{3}}ab^{3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-3\times 2a}{b^{3}}ab^{3}$$

Multiply -3 and 2 to get -6.

$$\frac{-6a}{b^{3}}ab^{3}$$

Express \frac{-6a}{b^{3}}a as a single fraction.

$$\frac{-6aa}{b^{3}}b^{3}$$

Cancel out b^{3} and b^{3}.

$$-6aa$$

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

$$-6a^{2}$$

Differentiate w.r.t. a

$$-12a$$

Steps Using Definition of a Derivative

Express 4\times \frac{-3a}{2b^{3}} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4\left(-3\right)a}{2b^{3}}ab^{3})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-3\times 2a}{b^{3}}ab^{3})$$

Multiply -3 and 2 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-6a}{b^{3}}ab^{3})$$

Express \frac{-6a}{b^{3}}a as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-6aa}{b^{3}}b^{3})$$

Cancel out b^{3} and b^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-6aa)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(-6a^{2})$$

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

$$2\left(-6\right)a^{2-1}$$

Multiply 2 times -6.

$$-12a^{2-1}$$

Subtract 1 from 2.

$$-12a^{1}$$

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

$$-12a$$