Solve 4xx^2+8x+7

$$4 x x ^ { 2 } + 8 x + 7$$

Differentiate w.r.t. x

$$12x^{2}+8$$

Steps Using Derivative Rule for Sum

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}+8x+7)$$

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}.

$$3\times 4x^{3-1}+8x^{1-1}$$

Multiply 3 times 4.

$$12x^{3-1}+8x^{1-1}$$

Subtract 1 from 3.

$$12x^{2}+8x^{1-1}$$

Subtract 1 from 1.

$$12x^{2}+8x^{0}$$

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

$$12x^{2}+8\times 1$$

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

$$12x^{2}+8$$

Evaluate

$$4x^{3}+8x+7$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$4x^{3}+8x+7$$