Solve (15x^3+8x)+(2x^2-6x+9)

$$(15 { x }^{ 3 } +8x)+(2 { x }^{ 2 } -6x+9)$$

Differentiate w.r.t. x

$$45x^{2}+4x+2$$

Steps Using Derivative Rule for Sum

Combine 8x and -6x to get 2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{3}+2x+2x^{2}+9)$$

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}.

$$3\times 15x^{3-1}+2x^{1-1}+2\times 2x^{2-1}$$

Multiply 3 times 15.

$$45x^{3-1}+2x^{1-1}+2\times 2x^{2-1}$$

Subtract 1 from 3.

$$45x^{2}+2x^{1-1}+2\times 2x^{2-1}$$

Subtract 1 from 1.

$$45x^{2}+2x^{0}+2\times 2x^{2-1}$$

Multiply 1 times 2.

$$45x^{2}+2x^{0}+4x^{2-1}$$

Subtract 1 from 2.

$$45x^{2}+2x^{0}+4x^{1}$$

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

$$45x^{2}+2x^{0}+4x$$

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

$$45x^{2}+2\times 1+4x$$

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

$$45x^{2}+2+4x$$

Evaluate

$$15x^{3}+2x^{2}+2x+9$$

Solution Steps

Combine 8x and -6x to get 2x.

$$15x^{3}+2x+2x^{2}+9$$