Solve 4x*3.5x+x^2=

$$4x \times 3.5x+ { x }^{ 2 } =$$

Evaluate

$$15x^{2}$$

Solution Steps

Multiply x and x to get x^{2}.

$$4x^{2}\times 3.5+x^{2}$$

Multiply 4 and 3.5 to get 14.

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

Combine 14x^{2} and x^{2} to get 15x^{2}.

$$15x^{2}$$

Differentiate w.r.t. x

$$30x$$

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}.

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

Subtract 1 from 1.

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

Subtract 1 from 2.

$$14xx^{0}+2x^{1}$$

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

$$14xx^{0}+2x$$

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

$$14x\times 1+2x$$

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

$$14x+2x$$