Solve 4x^3+8^2+2x+3

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

Evaluate

$$4x^{3}+2x+67$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$4x^{3}+64+2x+3$$

Add 64 and 3 to get 67.

$$4x^{3}+67+2x$$

Differentiate w.r.t. x

$$12x^{2}+2$$

Steps Using Derivative Rule for Sum

Calculate 8 to the power of 2 and get 64.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}+64+2x+3)$$

Add 64 and 3 to get 67.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}+67+2x)$$

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}.

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

Multiply 3 times 4.

$$12x^{3-1}+2x^{1-1}$$

Subtract 1 from 3.

$$12x^{2}+2x^{1-1}$$

Subtract 1 from 1.

$$12x^{2}+2x^{0}$$

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

$$12x^{2}+2\times 1$$

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

$$12x^{2}+2$$