Solve 3/2a^3b(-2/9)ab^2x(-1/2)b^3x^2

$$\frac { 3 } { 2 } a ^ { 3 } b ( - \frac { 2 } { 9 } ) a b ^ { 2 } x ( - \frac { 1 } { 2 } ) b ^ { 3 } x ^ { 2 }$$

Evaluate

$$\frac{x^{3}a^{4}b^{6}}{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{3}{2}a^{4}b\left(-\frac{2}{9}\right)b^{2}x\left(-\frac{1}{2}\right)b^{3}x^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{3}{2}a^{4}b^{3}\left(-\frac{2}{9}\right)x\left(-\frac{1}{2}\right)b^{3}x^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{3}{2}a^{4}b^{6}\left(-\frac{2}{9}\right)x\left(-\frac{1}{2}\right)x^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{3}{2}a^{4}b^{6}\left(-\frac{2}{9}\right)x^{3}\left(-\frac{1}{2}\right)$$

Multiply \frac{3}{2} and -\frac{2}{9} to get -\frac{1}{3}.

$$-\frac{1}{3}a^{4}b^{6}x^{3}\left(-\frac{1}{2}\right)$$

Multiply -\frac{1}{3} and -\frac{1}{2} to get \frac{1}{6}.

$$\frac{1}{6}a^{4}b^{6}x^{3}$$

Differentiate w.r.t. x

$$\frac{x^{2}a^{4}b^{6}}{2}$$