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

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

Evaluate

$$3x^{2}+3x+7$$

Solution Steps

Combine -x^{2} and 4x^{2} to get 3x^{2}.

$$3x+3x^{2}+5+2$$

Add 5 and 2 to get 7.

$$3x+3x^{2}+7$$

Differentiate w.r.t. x

$$6x+3$$

Steps Using Derivative Rule for Sum

Combine -x^{2} and 4x^{2} to get 3x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+3x^{2}+5+2)$$

Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+3x^{2}+7)$$

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}.

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

Subtract 1 from 1.

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

Multiply 2 times 3.

$$3x^{0}+6x^{2-1}$$

Subtract 1 from 2.

$$3x^{0}+6x^{1}$$

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

$$3x^{0}+6x$$

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

$$3\times 1+6x$$

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

$$3+6x$$