Solve 2x^2divx^3

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

Evaluate

$$\frac{2}{x}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 3 times -1.

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

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

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

Add the exponents 2 and -3.

$$2^{1}\times \frac{1}{1}\times \frac{1}{x}$$

Raise 2 to the power 1.

$$2\times \frac{1}{1}\times \frac{1}{x}$$

Differentiate w.r.t. x

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

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2\times \frac{1}{x})$$

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}.

$$-2x^{-1-1}$$

Do the arithmetic.

$$-2x^{-2}$$