Solve 12x^4/4x^2

$$\frac{ 12 { x }^{ 4 } }{ 4 { x }^{ 2 } }$$

Evaluate

$$3x^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(12x^{4}\right)^{1}\times \frac{1}{4x^{2}}$$

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

$$12^{1}\left(x^{4}\right)^{1}\times \frac{1}{4}\times \frac{1}{x^{2}}$$

Use the Commutative Property of Multiplication.

$$12^{1}\times \frac{1}{4}\left(x^{4}\right)^{1}\times \frac{1}{x^{2}}$$

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

$$12^{1}\times \frac{1}{4}x^{4}x^{2\left(-1\right)}$$

Multiply 2 times -1.

$$12^{1}\times \frac{1}{4}x^{4}x^{-2}$$

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

$$12^{1}\times \frac{1}{4}x^{4-2}$$

Add the exponents 4 and -2.

$$12^{1}\times \frac{1}{4}x^{2}$$

Raise 12 to the power 1.

$$12\times \frac{1}{4}x^{2}$$

Multiply 12 times \frac{1}{4}.

$$3x^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}x^{4}}{4^{1}x^{2}}$$

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

$$\frac{12^{1}x^{4-2}}{4^{1}}$$

Subtract 2 from 4.

$$\frac{12^{1}x^{2}}{4^{1}}$$

Divide 12 by 4.

$$3x^{2}$$

Differentiate w.r.t. x

$$6x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12}{4}x^{4-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2})$$

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}.

$$2\times 3x^{2-1}$$

Do the arithmetic.

$$6x^{1}$$

For any term t, t^{1}=t.

$$6x$$