Solve t^5-2t^2-1

$$t ^ { 5 } - 2 t ^ { 2 } - 1$$

Differentiate w.r.t. t

$$t\left(5t^{3}-4\right)$$

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}.

$$5t^{5-1}+2\left(-2\right)t^{2-1}$$

Subtract 1 from 5.

$$5t^{4}+2\left(-2\right)t^{2-1}$$

Multiply 2 times -2.

$$5t^{4}-4t^{2-1}$$

Subtract 1 from 2.

$$5t^{4}-4t^{1}$$

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

$$5t^{4}-4t$$

Evaluate

$$t^{5}-2t^{2}-1$$