Solve -4x^2divx^3

$$- 4 x ^ { 2 } \div x ^ { 3 }$$

Evaluate

$$-\frac{4}{x}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-4x^{2}\right)^{1}\times \frac{1}{x^{3}}$$

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

$$\left(-4\right)^{1}\left(x^{2}\right)^{1}\times \frac{1}{1}\times \frac{1}{x^{3}}$$

Use the Commutative Property of Multiplication.

$$\left(-4\right)^{1}\times \frac{1}{1}\left(x^{2}\right)^{1}\times \frac{1}{x^{3}}$$

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

$$\left(-4\right)^{1}\times \frac{1}{1}x^{2}x^{3\left(-1\right)}$$

Multiply 3 times -1.

$$\left(-4\right)^{1}\times \frac{1}{1}x^{2}x^{-3}$$

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

$$\left(-4\right)^{1}\times \frac{1}{1}x^{2-3}$$

Add the exponents 2 and -3.

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

Raise -4 to the power 1.

$$-4\times \frac{1}{1}\times \frac{1}{x}$$

Differentiate w.r.t. x

$$\frac{4}{x^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{4}{1}\right)x^{2-3})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$4x^{-2}$$