Solve x^2+8x+15x^2+8x+15

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

Evaluate

$$16x^{2}+16x+15$$

Solution Steps

Combine x^{2} and 15x^{2} to get 16x^{2}.

$$16x^{2}+8x+8x+15$$

Combine 8x and 8x to get 16x.

$$16x^{2}+16x+15$$

Differentiate w.r.t. x

$$32x+16$$

Steps Using Derivative Rule for Sum

Combine x^{2} and 15x^{2} to get 16x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{2}+8x+8x+15)$$

Combine 8x and 8x to get 16x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{2}+16x+15)$$

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}.

$$2\times 16x^{2-1}+16x^{1-1}$$

Multiply 2 times 16.

$$32x^{2-1}+16x^{1-1}$$

Subtract 1 from 2.

$$32x^{1}+16x^{1-1}$$

Subtract 1 from 1.

$$32x^{1}+16x^{0}$$

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

$$32x+16x^{0}$$

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

$$32x+16\times 1$$

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

$$32x+16$$