Solve 5x-2-6x^2+4x-3x^2+x-30

$$5x-2-6 { x }^{ 2 } +4x-3 { x }^{ 2 } +x-30$$

Evaluate

$$-9x^{2}+10x-32$$

Solution Steps

Combine 5x and 4x to get 9x.

$$9x-2-6x^{2}-3x^{2}+x-30$$

Combine -6x^{2} and -3x^{2} to get -9x^{2}.

$$9x-2-9x^{2}+x-30$$

Combine 9x and x to get 10x.

$$10x-2-9x^{2}-30$$

Subtract 30 from -2 to get -32.

$$10x-32-9x^{2}$$

Differentiate w.r.t. x

$$10-18x$$

Steps Using Derivative Rule for Sum

Combine 5x and 4x to get 9x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x-2-6x^{2}-3x^{2}+x-30)$$

Combine -6x^{2} and -3x^{2} to get -9x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x-2-9x^{2}+x-30)$$

Combine 9x and x to get 10x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x-2-9x^{2}-30)$$

Subtract 30 from -2 to get -32.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x-32-9x^{2})$$

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}.

$$10x^{1-1}+2\left(-9\right)x^{2-1}$$

Subtract 1 from 1.

$$10x^{0}+2\left(-9\right)x^{2-1}$$

Multiply 2 times -9.

$$10x^{0}-18x^{2-1}$$

Subtract 1 from 2.

$$10x^{0}-18x^{1}$$

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

$$10x^{0}-18x$$

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

$$10\times 1-18x$$

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

$$10-18x$$