Solve 15a^2-6ab-8a^2+6-5ab-9+a^2-ab

$$15 a ^ { 2 } - 6 a b - 8 a ^ { 2 } + 6 - 5 a b - 9 + a ^ { 2 } - a b$$

Evaluate

$$8a^{2}-12ab-3$$

Solution Steps

Combine 15a^{2} and -8a^{2} to get 7a^{2}.

$$7a^{2}-6ab+6-5ab-9+a^{2}-ab$$

Combine -6ab and -5ab to get -11ab.

$$7a^{2}-11ab+6-9+a^{2}-ab$$

Subtract 9 from 6 to get -3.

$$7a^{2}-11ab-3+a^{2}-ab$$

Combine 7a^{2} and a^{2} to get 8a^{2}.

$$8a^{2}-11ab-3-ab$$

Combine -11ab and -ab to get -12ab.

$$8a^{2}-12ab-3$$

Differentiate w.r.t. a

$$16a-12b$$

Steps Using Derivative Rule for Sum

Combine 15a^{2} and -8a^{2} to get 7a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(7a^{2}-6ab+6-5ab-9+a^{2}-ab)$$

Combine -6ab and -5ab to get -11ab.

$$\frac{\mathrm{d}}{\mathrm{d}a}(7a^{2}-11ab+6-9+a^{2}-ab)$$

Subtract 9 from 6 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}a}(7a^{2}-11ab-3+a^{2}-ab)$$

Combine 7a^{2} and a^{2} to get 8a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(8a^{2}-11ab-3-ab)$$

Combine -11ab and -ab to get -12ab.

$$\frac{\mathrm{d}}{\mathrm{d}a}(8a^{2}-12ab-3)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times 8a^{2-1}+\left(-12b\right)a^{1-1}$$

Multiply 2 times 8.

$$16a^{2-1}+\left(-12b\right)a^{1-1}$$

Subtract 1 from 2.

$$16a^{1}+\left(-12b\right)a^{1-1}$$

Subtract 1 from 1.

$$16a^{1}+\left(-12b\right)a^{0}$$

For any term t, t^{1}=t.

$$16a+\left(-12b\right)a^{0}$$

For any term t except 0, t^{0}=1.

$$16a+\left(-12b\right)\times 1$$

For any term t, t\times 1=t and 1t=t.

$$16a-12b$$