Solve -2/7ax^3(+21/8a^2x)(-2/9a^3)(+3/4ax)

$$- \frac { 2 } { 7 } a x ^ { 3 } ( + \frac { 21 } { 8 } a ^ { 2 } x ) ( - \frac { 2 } { 9 } a ^ { 3 } ) ( + \frac { 3 } { 4 } a x )$$

Evaluate

$$\frac{x^{5}a^{7}}{8}$$

Solution Steps

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

$$-\frac{2}{7}a^{3}x^{3}\times \frac{21}{8}x\left(-\frac{2}{9}\right)a^{3}\times \frac{3}{4}ax$$

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

$$-\frac{2}{7}a^{6}x^{3}\times \frac{21}{8}x\left(-\frac{2}{9}\right)\times \frac{3}{4}ax$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$-\frac{2}{7}a^{7}x^{3}\times \frac{21}{8}x\left(-\frac{2}{9}\right)\times \frac{3}{4}x$$

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

$$-\frac{2}{7}a^{7}x^{4}\times \frac{21}{8}\left(-\frac{2}{9}\right)\times \frac{3}{4}x$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$-\frac{2}{7}a^{7}x^{5}\times \frac{21}{8}\left(-\frac{2}{9}\right)\times \frac{3}{4}$$

Multiply -\frac{2}{7} and \frac{21}{8} to get -\frac{3}{4}.

$$-\frac{3}{4}a^{7}x^{5}\left(-\frac{2}{9}\right)\times \frac{3}{4}$$

Multiply -\frac{3}{4} and -\frac{2}{9} to get \frac{1}{6}.

$$\frac{1}{6}a^{7}x^{5}\times \frac{3}{4}$$

Multiply \frac{1}{6} and \frac{3}{4} to get \frac{1}{8}.

$$\frac{1}{8}a^{7}x^{5}$$

Differentiate w.r.t. x

$$\frac{5x^{4}a^{7}}{8}$$