Solve -12x^3/-3x^2

$$\frac { - 12 x ^ { 3 } } { - 3 x ^ { 2 } }$$

Evaluate

$$4x$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Use the Commutative Property of Multiplication.

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

To raise a power to another power, multiply the exponents.

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

Multiply 2 times -1.

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

To multiply powers of the same base, add their exponents.

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

Add the exponents 3 and -2.

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

Raise -12 to the power 1.

$$-12\times \frac{1}{-3}x^{1}$$

Raise -3 to the power -1.

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

Multiply -12 times -\frac{1}{3}.

$$4x^{1}$$

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

$$4x$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 2 from 3.

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

Divide -12 by -3.

$$4x^{1}$$

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

$$4x$$

Differentiate w.r.t. x

$$4$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{1})$$

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}.

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

Do the arithmetic.

$$4x^{0}$$

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

$$4\times 1$$

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

$$4$$