Solve a^{2}bc^5:[(-2b^3c^2)*(b^3c)]

$$a ^ { 2 } b c ^ { 5 } : [ ( - 2 b ^ { 3 } c ^ { 2 } ) \cdot ( b ^ { 3 } c ) ]$$

Evaluate

$$-\frac{\left(ac\right)^{2}}{2b^{5}}$$

Solution Steps

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

$$\frac{a^{2}bc^{5}}{-2b^{6}c^{2}c}$$

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

$$\frac{a^{2}bc^{5}}{-2b^{6}c^{3}}$$

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

$$\frac{a^{2}c^{2}}{-2b^{5}}$$

Differentiate w.r.t. a

$$-\frac{ac^{2}}{b^{5}}$$