Solve -ab^{3}cquad1,5a^5bc^2quada^2bc^3d

$$- a b ^ { 3 } c \quad 1,5 a ^ { 5 } b c ^ { 2 } \quad a ^ { 2 } b c ^ { 3 } d$$

Evaluate

$$-\frac{c_{1}da^{8}\left(bc\right)^{5}}{2}$$

Solution Steps

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

$$\left(-a\right)b^{4}c_{1}\times 0,5a^{5}c^{2}a^{2}bc^{3}d$$

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

$$\left(-a\right)b^{5}c_{1}\times 0,5a^{5}c^{2}a^{2}c^{3}d$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\left(-a\right)b^{5}c_{1}\times 0,5a^{7}c^{2}c^{3}d$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\left(-a\right)b^{5}c_{1}\times 0,5a^{7}c^{5}d$$

Multiply -1 and 0,5 to get -0,5.

$$-0,5ab^{5}c_{1}a^{7}c^{5}d$$

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$-0,5a^{8}b^{5}c_{1}c^{5}d$$

Differentiate w.r.t. c_1

$$-\frac{da^{8}\left(bc\right)^{5}}{2}$$