Solve x^2-12x+36quad6quad4x^2+12x+9

$$x ^ { 2 } - 12 x + 36 \quad 6 \quad 4 x ^ { 2 } + 12 x + 9$$

Evaluate

$$865x^{2}+9$$

Solution Steps

Multiply 36 and 6 to get 216.

$$x^{2}-12x+216\times 4x^{2}+12x+9$$

Multiply 216 and 4 to get 864.

$$x^{2}-12x+864x^{2}+12x+9$$

Combine x^{2} and 864x^{2} to get 865x^{2}.

$$865x^{2}-12x+12x+9$$

Combine -12x and 12x to get 0.

$$865x^{2}+9$$

Differentiate w.r.t. x

$$1730x$$

Steps Using Derivative Rule for Sum

Multiply 36 and 6 to get 216.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-12x+216\times 4x^{2}+12x+9)$$

Multiply 216 and 4 to get 864.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-12x+864x^{2}+12x+9)$$

Combine x^{2} and 864x^{2} to get 865x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(865x^{2}-12x+12x+9)$$

Combine -12x and 12x to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(865x^{2}+9)$$

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}.

$$2\times 865x^{2-1}$$

Multiply 2 times 865.

$$1730x^{2-1}$$

Subtract 1 from 2.

$$1730x^{1}$$

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

$$1730x$$