Solve pix^2+3x+01415926

$$\pi { x }^{ 2 } +3x+01415926$$

Evaluate

$$x\left(\pi x+3\right)$$

Solution Steps

Multiply 0 and 1415926 to get 0.

$$\pi x^{2}+3x+0$$

Anything plus zero gives itself.

$$\pi x^{2}+3x$$

Differentiate w.r.t. x

$$2\pi x+3$$

Steps Using Derivative Rule for Sum

Multiply 0 and 1415926 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\pi x^{2}+3x+0)$$

Anything plus zero gives itself.

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

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}.

$$2\pi x^{2-1}+3x^{1-1}$$

Subtract 1 from 2.

$$2\pi x^{1}+3x^{1-1}$$

Subtract 1 from 1.

$$2\pi x^{1}+3x^{0}$$

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

$$2\pi x+3x^{0}$$

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

$$2\pi x+3\times 1$$

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

$$2\pi x+3$$