Solve -x^3divx^2

$$- x ^ { 3 } \div x ^ { 2 }$$

Evaluate

$$-x$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times -1.

$$-\frac{1}{1}x^{3}x^{-2}$$

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

$$-\frac{1}{1}x^{3-2}$$

Add the exponents 3 and -2.

$$-\frac{1}{1}x^{1}$$

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

$$-\frac{1}{1}x$$

Differentiate w.r.t. x

$$-1$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-x^{0}$$

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

$$-1$$