Solve 7*62x^3-7x^2+2x+3

$$7 \cdot 62 x ^ { 3 } - 7 x ^ { 2 } + 2 x + 3$$

Differentiate w.r.t. x

$$1302x^{2}-14x+2$$

Steps Using Derivative Rule for Sum

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}.

$$3\times 434x^{3-1}+2\left(-7\right)x^{2-1}+2x^{1-1}$$

Multiply 3 times 7\times 62.

$$1302x^{3-1}+2\left(-7\right)x^{2-1}+2x^{1-1}$$

Subtract 1 from 3.

$$1302x^{2}+2\left(-7\right)x^{2-1}+2x^{1-1}$$

Multiply 2 times -7.

$$1302x^{2}-14x^{2-1}+2x^{1-1}$$

Subtract 1 from 2.

$$1302x^{2}-14x^{1}+2x^{1-1}$$

Subtract 1 from 1.

$$1302x^{2}-14x^{1}+2x^{0}$$

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

$$1302x^{2}-14x+2x^{0}$$

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

$$1302x^{2}-14x+2\times 1$$

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

$$1302x^{2}-14x+2$$

Evaluate

$$434x^{3}-7x^{2}+2x+3$$

Solution Steps

Multiply 7 and 62 to get 434.

$$434x^{3}-7x^{2}+2x+3$$