Solve 12d^2/4d

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

Evaluate

$$3d$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 1 from 2.

$$\frac{12^{1}d^{1}}{4^{1}}$$

Divide 12 by 4.

$$3d^{1}$$

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

$$3d$$

Differentiate w.r.t. d

$$3$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{12}{4}d^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}d}(3d^{1})$$

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}.

$$3d^{1-1}$$

Do the arithmetic.

$$3d^{0}$$

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

$$3\times 1$$

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

$$3$$