Solve 4b^2/2b=

$$\frac { 4 b ^ { 2 } } { 2 b } =$$

Evaluate

$$2b$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{4^{1}b^{2}}{2^{1}b^{1}}$$

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

$$\frac{4^{1}b^{2-1}}{2^{1}}$$

Subtract 1 from 2.

$$\frac{4^{1}b^{1}}{2^{1}}$$

Divide 4 by 2.

$$2b^{1}$$

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

$$2b$$

Differentiate w.r.t. b

$$2$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{4}{2}b^{2-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$2b^{0}$$

For any term t except 0, t^{0}=1.

$$2\times 1$$

For any term t, t\times 1=t and 1t=t.

$$2$$