Solve 8x^2+4x-5-12x^2

$$8 x ^ { 2 } + 4 x - 5 - 12 x ^ { 2 }$$

Differentiate w.r.t. x

$$4-8x$$

Steps Using Derivative Rule for Sum

Combine 8x^{2} and -12x^{2} to get -4x^{2}.

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

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}.

$$2\left(-4\right)x^{2-1}+4x^{1-1}$$

Multiply 2 times -4.

$$-8x^{2-1}+4x^{1-1}$$

Subtract 1 from 2.

$$-8x^{1}+4x^{1-1}$$

Subtract 1 from 1.

$$-8x^{1}+4x^{0}$$

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

$$-8x+4x^{0}$$

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

$$-8x+4\times 1$$

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

$$-8x+4$$

Evaluate

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

Solution Steps

Combine 8x^{2} and -12x^{2} to get -4x^{2}.

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