Solve 5a^2-7a^2+3a^2-2a^2

$$5 a ^ { 2 } - 7 a ^ { 2 } + 3 a ^ { 2 } - 2 a ^ { 2 }$$

Evaluate

$$-a^{2}$$

Solution Steps

Combine 5a^{2} and -7a^{2} to get -2a^{2}.

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

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

$$a^{2}-2a^{2}$$

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

$$-a^{2}$$

Differentiate w.r.t. a

$$-2a$$

Steps Using Definition of a Derivative

Combine 5a^{2} and -7a^{2} to get -2a^{2}.

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

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

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

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

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

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

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

Multiply 2 times -1.

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

Subtract 1 from 2.

$$-2a^{1}$$

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

$$-2a$$