Solve 6x^3+4+2x^2*15+x^2

$$6 { x }^{ 3 } +4+2 { x }^{ 2 } \times 15+ { x }^{ 2 }$$

Evaluate

$$6x^{3}+31x^{2}+4$$

Solution Steps

Multiply 2 and 15 to get 30.

$$6x^{3}+4+30x^{2}+x^{2}$$

Combine 30x^{2} and x^{2} to get 31x^{2}.

$$6x^{3}+4+31x^{2}$$

Differentiate w.r.t. x

$$2x\left(9x+31\right)$$

Steps Using Derivative Rule for Sum

Multiply 2 and 15 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3}+4+30x^{2}+x^{2})$$

Combine 30x^{2} and x^{2} to get 31x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3}+4+31x^{2})$$

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}.

$$3\times 6x^{3-1}+2\times 31x^{2-1}$$

Multiply 3 times 6.

$$18x^{3-1}+2\times 31x^{2-1}$$

Subtract 1 from 3.

$$18x^{2}+2\times 31x^{2-1}$$

Multiply 2 times 31.

$$18x^{2}+62x^{2-1}$$

Subtract 1 from 2.

$$18x^{2}+62x^{1}$$

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

$$18x^{2}+62x$$