Solve 2b^1/b^-1

$$\frac { 2 b ^ { 1 } } { b ^ { - 1 } }$$

Evaluate

$$2b^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2b^{1}\right)^{1}\times \frac{1}{\frac{1}{b}}$$

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

$$2^{1}\left(b^{1}\right)^{1}\times \frac{1}{1}\times \frac{1}{\frac{1}{b}}$$

Use the Commutative Property of Multiplication.

$$2^{1}\times \frac{1}{1}\left(b^{1}\right)^{1}\times \frac{1}{\frac{1}{b}}$$

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

$$2^{1}\times \frac{1}{1}b^{1}b^{-\left(-1\right)}$$

Multiply -1 times -1.

$$2^{1}\times \frac{1}{1}b^{1}b^{1}$$

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

$$2^{1}\times \frac{1}{1}b^{1+1}$$

Add the exponents 1 and 1.

$$2^{1}\times \frac{1}{1}b^{2}$$

Raise 2 to the power 1.

$$2\times \frac{1}{1}b^{2}$$

Differentiate w.r.t. b

$$4b$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{2}{1}b^{1-\left(-1\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b^{2})$$

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}.

$$2\times 2b^{2-1}$$

Do the arithmetic.

$$4b^{1}$$

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

$$4b$$