Solve 3x^3div-x^4

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

Evaluate

$$-\frac{3}{x}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 4 times -1.

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

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

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

Add the exponents 3 and -4.

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

Raise 3 to the power 1.

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

Multiply 3 times -1.

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

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 4 from 3.

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

Divide 3 by -1.

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

Differentiate w.r.t. x

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

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$3x^{-2}$$