Solve (-3a^{3}-7ab+5a^{2}b^{2})+(-3a^3-7ab-5a^2b^2)+(-3a^3+14ab)

$$( - 3 a ^ { 3 } - 7 a b + 5 a ^ { 2 } b ^ { 2 } ) + ( - 3 a ^ { 3 } - 7 a b - 5 a ^ { 2 } b ^ { 2 } ) + ( - 3 a ^ { 3 } + 14 a b )$$

Evaluate

$$-9a^{3}$$

Solution Steps

Combine -3a^{3} and -3a^{3} to get -6a^{3}.

$$-6a^{3}-7ab+5a^{2}b^{2}+-3a^{3}-7ab-5a^{2}b^{2}+14ab$$

Combine -7ab and 14ab to get 7ab.

$$-6a^{3}+7ab+5a^{2}b^{2}+-3a^{3}-7ab-5a^{2}b^{2}$$

Combine -6a^{3} and -3a^{3} to get -9a^{3}.

$$-9a^{3}+7ab+5a^{2}b^{2}-7ab-5a^{2}b^{2}$$

Combine 7ab and -7ab to get 0.

$$-9a^{3}+5a^{2}b^{2}-5a^{2}b^{2}$$

Combine 5a^{2}b^{2} and -5a^{2}b^{2} to get 0.

$$-9a^{3}$$

Differentiate w.r.t. a

$$-27a^{2}$$

Steps Using Definition of a Derivative

Combine -3a^{3} and -3a^{3} to get -6a^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-6a^{3}-7ab+5a^{2}b^{2}+-3a^{3}-7ab-5a^{2}b^{2}+14ab)$$

Combine -7ab and 14ab to get 7ab.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-6a^{3}+7ab+5a^{2}b^{2}+-3a^{3}-7ab-5a^{2}b^{2})$$

Combine -6a^{3} and -3a^{3} to get -9a^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-9a^{3}+7ab+5a^{2}b^{2}-7ab-5a^{2}b^{2})$$

Combine 7ab and -7ab to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-9a^{3}+5a^{2}b^{2}-5a^{2}b^{2})$$

Combine 5a^{2}b^{2} and -5a^{2}b^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-9a^{3})$$

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

$$3\left(-9\right)a^{3-1}$$

Multiply 3 times -9.

$$-27a^{3-1}$$

Subtract 1 from 3.

$$-27a^{2}$$