Solve 17+16t+4t^4

$$17 + 16 t + 4 t ^ { 4 }$$

Differentiate w.r.t. t

$$16\left(t^{3}+1\right)$$

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}.

$$16t^{1-1}+4\times 4t^{4-1}$$

Subtract 1 from 1.

$$16t^{0}+4\times 4t^{4-1}$$

Multiply 4 times 4.

$$16t^{0}+16t^{4-1}$$

Subtract 1 from 4.

$$16t^{0}+16t^{3}$$

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

$$16\times 1+16t^{3}$$

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

$$16+16t^{3}$$

Evaluate

$$4t^{4}+16t+17$$