Solve -t^2+3θt-12

$$- t ^ { 2 } + 3 \theta t - 12$$

Differentiate w.r.t. t

$$3\theta -2t$$

Steps Using Derivative Rule for Sum

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}.

$$2\left(-1\right)t^{2-1}+3\theta t^{1-1}$$

Multiply 2 times -1.

$$-2t^{2-1}+3\theta t^{1-1}$$

Subtract 1 from 2.

$$-2t^{1}+3\theta t^{1-1}$$

Subtract 1 from 1.

$$-2t^{1}+3\theta t^{0}$$

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

$$-2t+3\theta t^{0}$$

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

$$-2t+3\theta \times 1$$

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

$$-2t+3\theta$$

Evaluate

$$-t^{2}+3t\theta -12$$