Solve Delta24/27+1^2

$$\frac { \Delta 24 } { 27 + 1 ^ { 2 } }$$

Evaluate

$$\frac{\Delta _{24}}{28}$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$\frac{\Delta _{24}}{27+1}$$

Add 27 and 1 to get 28.

$$\frac{\Delta _{24}}{28}$$

Differentiate w.r.t. Δ_24

$$\frac{1}{28} = 0.03571428571428571$$

Steps Using Definition of a Derivative

Calculate 1 to the power of 2 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}\Delta _{24}}(\frac{\Delta _{24}}{27+1})$$

Add 27 and 1 to get 28.

$$\frac{\mathrm{d}}{\mathrm{d}\Delta _{24}}(\frac{\Delta _{24}}{28})$$

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

$$\frac{1}{28}\Delta _{24}^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{28}\Delta _{24}^{0}$$

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

$$\frac{1}{28}\times 1$$

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

$$\frac{1}{28}$$