Solve 12x^6/42x^4

$$\frac { 12 x ^ { 6 } } { 42 x ^ { 4 } }$$

Evaluate

$$\frac{2x^{2}}{7}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(12x^{6}\right)^{1}\times \frac{1}{42x^{4}}$$

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

$$12^{1}\left(x^{6}\right)^{1}\times \frac{1}{42}\times \frac{1}{x^{4}}$$

Use the Commutative Property of Multiplication.

$$12^{1}\times \frac{1}{42}\left(x^{6}\right)^{1}\times \frac{1}{x^{4}}$$

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

$$12^{1}\times \frac{1}{42}x^{6}x^{4\left(-1\right)}$$

Multiply 4 times -1.

$$12^{1}\times \frac{1}{42}x^{6}x^{-4}$$

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

$$12^{1}\times \frac{1}{42}x^{6-4}$$

Add the exponents 6 and -4.

$$12^{1}\times \frac{1}{42}x^{2}$$

Raise 12 to the power 1.

$$12\times \frac{1}{42}x^{2}$$

Multiply 12 times \frac{1}{42}.

$$\frac{2}{7}x^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}x^{6}}{42^{1}x^{4}}$$

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

$$\frac{12^{1}x^{6-4}}{42^{1}}$$

Subtract 4 from 6.

$$\frac{12^{1}x^{2}}{42^{1}}$$

Reduce the fraction \frac{12}{42} to lowest terms by extracting and canceling out 6.

$$\frac{2}{7}x^{2}$$

Differentiate w.r.t. x

$$\frac{4x}{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12}{42}x^{6-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{7}x^{2})$$

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}.

$$2\times \frac{2}{7}x^{2-1}$$

Do the arithmetic.

$$\frac{4}{7}x^{1}$$

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

$$\frac{4}{7}x$$