Solve -208x/-x^2

$$\frac{ -208x }{ - { x }^{ 2 } }$$

Evaluate

$$\frac{208}{x}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-208x^{1}\right)^{1}\times \frac{1}{-x^{2}}$$

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

$$\left(-208\right)^{1}\left(x^{1}\right)^{1}\left(-1\right)\times \frac{1}{x^{2}}$$

Use the Commutative Property of Multiplication.

$$\left(-208\right)^{1}\left(-1\right)\left(x^{1}\right)^{1}\times \frac{1}{x^{2}}$$

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

$$\left(-208\right)^{1}\left(-1\right)x^{1}x^{2\left(-1\right)}$$

Multiply 2 times -1.

$$\left(-208\right)^{1}\left(-1\right)x^{1}x^{-2}$$

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

$$\left(-208\right)^{1}\left(-1\right)x^{1-2}$$

Add the exponents 1 and -2.

$$\left(-208\right)^{1}\left(-1\right)\times \frac{1}{x}$$

Raise -208 to the power 1.

$$-208\left(-1\right)\times \frac{1}{x}$$

Multiply -208 times -1.

$$208\times \frac{1}{x}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-208\right)^{1}x^{1}}{-x^{2}}$$

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

$$\frac{\left(-208\right)^{1}x^{1-2}}{-1}$$

Subtract 2 from 1.

$$\frac{\left(-208\right)^{1}\times \frac{1}{x}}{-1}$$

Divide -208 by -1.

$$208\times \frac{1}{x}$$

Differentiate w.r.t. x

$$-\frac{208}{x^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{208}{-1}\right)x^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(208\times \frac{1}{x})$$

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}.

$$-208x^{-1-1}$$

Do the arithmetic.

$$-208x^{-2}$$