Solve 10x^3divx^4

$$10 x ^ { 3 } \div x ^ { 4 }$$

Evaluate

$$\frac{10}{x}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(10x^{3}\right)^{1}\times \frac{1}{x^{4}}$$

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

$$10^{1}\left(x^{3}\right)^{1}\times \frac{1}{1}\times \frac{1}{x^{4}}$$

Use the Commutative Property of Multiplication.

$$10^{1}\times \frac{1}{1}\left(x^{3}\right)^{1}\times \frac{1}{x^{4}}$$

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

$$10^{1}\times \frac{1}{1}x^{3}x^{4\left(-1\right)}$$

Multiply 4 times -1.

$$10^{1}\times \frac{1}{1}x^{3}x^{-4}$$

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

$$10^{1}\times \frac{1}{1}x^{3-4}$$

Add the exponents 3 and -4.

$$10^{1}\times \frac{1}{1}\times \frac{1}{x}$$

Raise 10 to the power 1.

$$10\times \frac{1}{1}\times \frac{1}{x}$$

Differentiate w.r.t. x

$$-\frac{10}{x^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10}{1}x^{3-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10\times \frac{1}{x})$$

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}.

$$-10x^{-1-1}$$

Do the arithmetic.

$$-10x^{-2}$$