Solve 14x^13/x^14

$$\frac { 14 x ^ { 13 } } { x ^ { 14 } }$$

Evaluate

$$\frac{14}{x}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(14x^{13}\right)^{1}\times \frac{1}{x^{14}}$$

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

$$14^{1}\left(x^{13}\right)^{1}\times \frac{1}{1}\times \frac{1}{x^{14}}$$

Use the Commutative Property of Multiplication.

$$14^{1}\times \frac{1}{1}\left(x^{13}\right)^{1}\times \frac{1}{x^{14}}$$

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

$$14^{1}\times \frac{1}{1}x^{13}x^{14\left(-1\right)}$$

Multiply 14 times -1.

$$14^{1}\times \frac{1}{1}x^{13}x^{-14}$$

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

$$14^{1}\times \frac{1}{1}x^{13-14}$$

Add the exponents 13 and -14.

$$14^{1}\times \frac{1}{1}\times \frac{1}{x}$$

Raise 14 to the power 1.

$$14\times \frac{1}{1}\times \frac{1}{x}$$

Differentiate w.r.t. x

$$-\frac{14}{x^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{14}{1}x^{13-14})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(14\times \frac{1}{x})$$

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}.

$$-14x^{-1-1}$$

Do the arithmetic.

$$-14x^{-2}$$