Solve x+2x^2+12^3

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

Differentiate w.r.t. x

$$4x+1$$

Steps Using Derivative Rule for Sum

Calculate 12 to the power of 3 and get 1728.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+2x^{2}+1728)$$

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}.

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

Subtract 1 from 1.

$$x^{0}+2\times 2x^{2-1}$$

Multiply 2 times 2.

$$x^{0}+4x^{2-1}$$

Subtract 1 from 2.

$$x^{0}+4x^{1}$$

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

$$x^{0}+4x$$

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

$$1+4x$$

Evaluate

$$2x^{2}+x+1728$$

Solution Steps

Calculate 12 to the power of 3 and get 1728.

$$x+2x^{2}+1728$$