Solve 3x^2+12x+11+14x^2+8x+5

$$3 x ^ { 2 } + 12 x + 11 + 14 x ^ { 2 } + 8 x + 5$$

Evaluate

$$17x^{2}+20x+16$$

Solution Steps

Combine 3x^{2} and 14x^{2} to get 17x^{2}.

$$17x^{2}+12x+11+8x+5$$

Combine 12x and 8x to get 20x.

$$17x^{2}+20x+11+5$$

Add 11 and 5 to get 16.

$$17x^{2}+20x+16$$

Differentiate w.r.t. x

$$34x+20$$

Steps Using Derivative Rule for Sum

Combine 3x^{2} and 14x^{2} to get 17x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(17x^{2}+12x+11+8x+5)$$

Combine 12x and 8x to get 20x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(17x^{2}+20x+11+5)$$

Add 11 and 5 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(17x^{2}+20x+16)$$

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}.

$$2\times 17x^{2-1}+20x^{1-1}$$

Multiply 2 times 17.

$$34x^{2-1}+20x^{1-1}$$

Subtract 1 from 2.

$$34x^{1}+20x^{1-1}$$

Subtract 1 from 1.

$$34x^{1}+20x^{0}$$

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

$$34x+20x^{0}$$

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

$$34x+20\times 1$$

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

$$34x+20$$