Solve 10x^2+5-x^2+3-4

$$10 { x }^{ 2 } +5- { x }^{ 2 } +3-4$$

Evaluate

$$9x^{2}+4$$

Solution Steps

Combine 10x^{2} and -x^{2} to get 9x^{2}.

$$9x^{2}+5+3-4$$

Add 5 and 3 to get 8.

$$9x^{2}+8-4$$

Subtract 4 from 8 to get 4.

$$9x^{2}+4$$

Differentiate w.r.t. x

$$18x$$

Steps Using Derivative Rule for Sum

Combine 10x^{2} and -x^{2} to get 9x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{2}+5+3-4)$$

Add 5 and 3 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{2}+8-4)$$

Subtract 4 from 8 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{2}+4)$$

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}.

$$2\times 9x^{2-1}$$

Multiply 2 times 9.

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

Subtract 1 from 2.

$$18x^{1}$$

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

$$18x$$