Solve f(x)=5x^3+4x^2+8x+1.text{when}x=2

$$f ( x ) = 5 x ^ { 3 } + 4 x ^ { 2 } + 8 x + 1 . \text { when } x = 2$$

Differentiate w.r.t. x

$$15x^{2}+8x+8$$

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}.

$$3\times 5x^{3-1}+2\times 4x^{2-1}+8x^{1-1}$$

Multiply 3 times 5.

$$15x^{3-1}+2\times 4x^{2-1}+8x^{1-1}$$

Subtract 1 from 3.

$$15x^{2}+2\times 4x^{2-1}+8x^{1-1}$$

Multiply 2 times 4.

$$15x^{2}+8x^{2-1}+8x^{1-1}$$

Subtract 1 from 2.

$$15x^{2}+8x^{1}+8x^{1-1}$$

Subtract 1 from 1.

$$15x^{2}+8x^{1}+8x^{0}$$

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

$$15x^{2}+8x+8x^{0}$$

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

$$15x^{2}+8x+8\times 1$$

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

$$15x^{2}+8x+8$$

Evaluate

$$5x^{3}+4x^{2}+8x+1$$