Solve 3x^4/6x^-2

$$\frac { 3 x ^ { 4 } } { 6 x ^ { - 2 } }$$

Evaluate

$$\frac{x^{6}}{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(3x^{4}\right)^{1}\times \frac{1}{6x^{-2}}$$

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

$$3^{1}\left(x^{4}\right)^{1}\times \frac{1}{6}\times \frac{1}{x^{-2}}$$

Use the Commutative Property of Multiplication.

$$3^{1}\times \frac{1}{6}\left(x^{4}\right)^{1}\times \frac{1}{x^{-2}}$$

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

$$3^{1}\times \frac{1}{6}x^{4}x^{-2\left(-1\right)}$$

Multiply -2 times -1.

$$3^{1}\times \frac{1}{6}x^{4}x^{2}$$

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

$$3^{1}\times \frac{1}{6}x^{4+2}$$

Add the exponents 4 and 2.

$$3^{1}\times \frac{1}{6}x^{6}$$

Raise 3 to the power 1.

$$3\times \frac{1}{6}x^{6}$$

Multiply 3 times \frac{1}{6}.

$$\frac{1}{2}x^{6}$$

Differentiate w.r.t. x

$$3x^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{6}x^{4-\left(-2\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{6})$$

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}.

$$6\times \frac{1}{2}x^{6-1}$$

Do the arithmetic.

$$3x^{5}$$