Solve -3x^2*4x^2-x+1

$$- 3 x ^ { 2 } \times 4 x ^ { 2 } - x + 1$$

Evaluate

$$1-x-12x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-3x^{4}\times 4-x+1$$

Multiply -3 and 4 to get -12.

$$-12x^{4}-x+1$$

Differentiate w.r.t. x

$$-48x^{3}-1$$

Steps Using Derivative Rule for Sum

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}.

$$2\left(-12x^{2}\right)x^{2-1}-x^{1-1}$$

Multiply 2 times -3\times 4x^{2}.

$$\left(-24x^{2}\right)x^{2-1}-x^{1-1}$$

Subtract 1 from 2.

$$\left(-24x^{2}\right)x^{1}-x^{1-1}$$

Subtract 1 from 1.

$$\left(-24x^{2}\right)x^{1}-x^{0}$$

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

$$\left(-24x^{2}\right)x-x^{0}$$

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

$$\left(-24x^{2}\right)x-1$$