Solve -(-3a^2)+(-5a^2)-a-(-a)

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

Evaluate

$$-2a^{2}$$

Solution Steps

The opposite of -3a^{2} is 3a^{2}.

$$3a^{2}-5a^{2}-a-\left(-a\right)$$

Combine 3a^{2} and -5a^{2} to get -2a^{2}.

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

Multiply -1 and -1 to get 1.

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

Combine -a and a to get 0.

$$-2a^{2}$$

Differentiate w.r.t. a

$$-4a$$

Steps Using Definition of a Derivative

The opposite of -3a^{2} is 3a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{2}-5a^{2}-a-\left(-a\right))$$

Combine 3a^{2} and -5a^{2} to get -2a^{2}.

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

Multiply -1 and -1 to get 1.

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

Combine -a and a to get 0.

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

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

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

Multiply 2 times -2.

$$-4a^{2-1}$$

Subtract 1 from 2.

$$-4a^{1}$$

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

$$-4a$$