Solve 2x+3+4x^2-5x+6

$$2 x + 3 + 4 x ^ { 2 } - 5 x + 6$$

Evaluate

$$4x^{2}-3x+9$$

Solution Steps

Combine 2x and -5x to get -3x.

$$-3x+3+4x^{2}+6$$

Add 3 and 6 to get 9.

$$-3x+9+4x^{2}$$

Differentiate w.r.t. x

$$8x-3$$

Steps Using Derivative Rule for Sum

Combine 2x and -5x to get -3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x+3+4x^{2}+6)$$

Add 3 and 6 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x+9+4x^{2})$$

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}.

$$-3x^{1-1}+2\times 4x^{2-1}$$

Subtract 1 from 1.

$$-3x^{0}+2\times 4x^{2-1}$$

Multiply 2 times 4.

$$-3x^{0}+8x^{2-1}$$

Subtract 1 from 2.

$$-3x^{0}+8x^{1}$$

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

$$-3x^{0}+8x$$

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

$$-3+8x$$