Solve dlog_{2}2^5

$$d \log _ { 2 } 2 ^ { 5 }$$

Evaluate

$$5d$$

Solution Steps

Calculate 2 to the power of 5 and get 32.

$$d\log_{2}\left(32\right)$$

The base 2 logarithm of 32 is 5.

$$d\times 5$$

Differentiate w.r.t. d

$$5$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 5 and get 32.

$$\frac{\mathrm{d}}{\mathrm{d}d}(d\log_{2}\left(32\right))$$

The base 2 logarithm of 32 is 5.

$$\frac{\mathrm{d}}{\mathrm{d}d}(d\times 5)$$

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

$$5d^{1-1}$$

Subtract 1 from 1.

$$5d^{0}$$

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

$$5\times 1$$

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

$$5$$