Solve 3+24x+7x^2+16x^3

$$3 + 24 x + 7 x ^ { 2 } + 16 x ^ { 3 }$$

Differentiate w.r.t. x

$$48x^{2}+14x+24$$

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}.

$$24x^{1-1}+2\times 7x^{2-1}+3\times 16x^{3-1}$$

Subtract 1 from 1.

$$24x^{0}+2\times 7x^{2-1}+3\times 16x^{3-1}$$

Multiply 2 times 7.

$$24x^{0}+14x^{2-1}+3\times 16x^{3-1}$$

Subtract 1 from 2.

$$24x^{0}+14x^{1}+3\times 16x^{3-1}$$

Multiply 2 times 7.

$$24x^{0}+14x^{1}+48x^{3-1}$$

Subtract 1 from 3.

$$24x^{0}+14x^{1}+48x^{2}$$

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

$$24x^{0}+14x+48x^{2}$$

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

$$24\times 1+14x+48x^{2}$$

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

$$24+14x+48x^{2}$$

Evaluate

$$16x^{3}+7x^{2}+24x+3$$