Solve 40x^4/12x^2

$$\frac { 40 x ^ { 4 } } { 12 x ^ { 2 } }$$

Evaluate

$$\frac{10x^{2}}{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(40x^{4}\right)^{1}\times \frac{1}{12x^{2}}$$

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

$$40^{1}\left(x^{4}\right)^{1}\times \frac{1}{12}\times \frac{1}{x^{2}}$$

Use the Commutative Property of Multiplication.

$$40^{1}\times \frac{1}{12}\left(x^{4}\right)^{1}\times \frac{1}{x^{2}}$$

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

$$40^{1}\times \frac{1}{12}x^{4}x^{2\left(-1\right)}$$

Multiply 2 times -1.

$$40^{1}\times \frac{1}{12}x^{4}x^{-2}$$

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

$$40^{1}\times \frac{1}{12}x^{4-2}$$

Add the exponents 4 and -2.

$$40^{1}\times \frac{1}{12}x^{2}$$

Raise 40 to the power 1.

$$40\times \frac{1}{12}x^{2}$$

Multiply 40 times \frac{1}{12}.

$$\frac{10}{3}x^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{40^{1}x^{4}}{12^{1}x^{2}}$$

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

$$\frac{40^{1}x^{4-2}}{12^{1}}$$

Subtract 2 from 4.

$$\frac{40^{1}x^{2}}{12^{1}}$$

Reduce the fraction \frac{40}{12} to lowest terms by extracting and canceling out 4.

$$\frac{10}{3}x^{2}$$

Differentiate w.r.t. x

$$\frac{20x}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{40}{12}x^{4-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10}{3}x^{2})$$

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}.

$$2\times \frac{10}{3}x^{2-1}$$

Do the arithmetic.

$$\frac{20}{3}x^{1}$$

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

$$\frac{20}{3}x$$