Solve t^4-4t^2+16

$$t ^ { 4 } - 4 t ^ { 2 } + 16$$

Differentiate w.r.t. t

$$4t\left(t^{2}-2\right)$$

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}.

$$4t^{4-1}+2\left(-4\right)t^{2-1}$$

Subtract 1 from 4.

$$4t^{3}+2\left(-4\right)t^{2-1}$$

Multiply 2 times -4.

$$4t^{3}-8t^{2-1}$$

Subtract 1 from 2.

$$4t^{3}-8t^{1}$$

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

$$4t^{3}-8t$$

Evaluate

$$t^{4}-4t^{2}+16$$