Solve a^{2}+b^{2}-2b^2-3a^2-a^2+b^2

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

Evaluate

$$-3a^{2}$$

Solution Steps

Combine b^{2} and -2b^{2} to get -b^{2}.

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

Combine a^{2} and -3a^{2} to get -2a^{2}.

$$-2a^{2}-b^{2}-a^{2}+b^{2}$$

Combine -2a^{2} and -a^{2} to get -3a^{2}.

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

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

$$-3a^{2}$$

Differentiate w.r.t. a

$$-6a$$

Steps Using Definition of a Derivative

Combine b^{2} and -2b^{2} to get -b^{2}.

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

Combine a^{2} and -3a^{2} to get -2a^{2}.

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

Combine -2a^{2} and -a^{2} to get -3a^{2}.

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

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

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

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

$$2\left(-3\right)a^{2-1}$$

Multiply 2 times -3.

$$-6a^{2-1}$$

Subtract 1 from 2.

$$-6a^{1}$$

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

$$-6a$$