Solve 22^2/2d

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

Evaluate

$$4d$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$2\times 2^{1}d$$

To multiply powers of the same base, add their exponents. Add 1 and 1 to get 2.

$$2^{2}d$$

Calculate 2 to the power of 2 and get 4.

$$4d$$

Differentiate w.r.t. d

$$4$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

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

To multiply powers of the same base, add their exponents. Add 1 and 1 to get 2.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}d}(4d)$$

The derivative of ax^{n} is nax^{n-1}.

$$4d^{1-1}$$

Subtract 1 from 1.

$$4d^{0}$$

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

$$4\times 1$$

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

$$4$$