Solve 216-756a^2+882a^2-343a^2

$$216 - 756 a ^ { 2 } + 882 a ^ { 2 } - 343 a ^ { 2 }$$

Evaluate

$$216-217a^{2}$$

Solution Steps

Combine -756a^{2} and 882a^{2} to get 126a^{2}.

$$216+126a^{2}-343a^{2}$$

Combine 126a^{2} and -343a^{2} to get -217a^{2}.

$$216-217a^{2}$$

Differentiate w.r.t. a

$$-434a$$

Steps Using Derivative Rule for Sum

Combine -756a^{2} and 882a^{2} to get 126a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(216+126a^{2}-343a^{2})$$

Combine 126a^{2} and -343a^{2} to get -217a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(216-217a^{2})$$

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}.

$$2\left(-217\right)a^{2-1}$$

Multiply 2 times -217.

$$-434a^{2-1}$$

Subtract 1 from 2.

$$-434a^{1}$$

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

$$-434a$$