Solve 12x^3/-3x

$$\frac{ 12 { x }^{ 3 } }{ -3x }$$

Evaluate

$$-4x^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}x^{3}}{\left(-3\right)^{1}x^{1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{12^{1}x^{3-1}}{\left(-3\right)^{1}}$$

Subtract 1 from 3.

$$\frac{12^{1}x^{2}}{\left(-3\right)^{1}}$$

Divide 12 by -3.

$$-4x^{2}$$

Differentiate w.r.t. x

$$-8x$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12}{-3}x^{3-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-8x^{1}$$

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

$$-8x$$