Solve 3x^2-3+8x+4-8x-5x^2

$$3 { x }^{ 2 } -3+8x+4-8x-5 { x }^{ 2 }$$

Evaluate

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

Solution Steps

Add -3 and 4 to get 1.

$$3x^{2}+1+8x-8x-5x^{2}$$

Combine 8x and -8x to get 0.

$$3x^{2}+1-5x^{2}$$

Combine 3x^{2} and -5x^{2} to get -2x^{2}.

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

Differentiate w.r.t. x

$$-4x$$

Steps Using Derivative Rule for Sum

Add -3 and 4 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}+1+8x-8x-5x^{2})$$

Combine 8x and -8x to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}+1-5x^{2})$$

Combine 3x^{2} and -5x^{2} to get -2x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{2}+1)$$

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}.

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

Multiply 2 times -2.

$$-4x^{2-1}$$

Subtract 1 from 2.

$$-4x^{1}$$

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

$$-4x$$