Solve d/sqrt{61^2-11^2}

$$d / \sqrt { 61 ^ { 2 } - 11 ^ { 2 } }$$

Evaluate

$$\frac{d}{60}$$

Solution Steps

Calculate 61 to the power of 2 and get 3721.

$$\frac{d}{\sqrt{3721-11^{2}}}$$

Calculate 11 to the power of 2 and get 121.

$$\frac{d}{\sqrt{3721-121}}$$

Subtract 121 from 3721 to get 3600.

$$\frac{d}{\sqrt{3600}}$$

Calculate the square root of 3600 and get 60.

$$\frac{d}{60}$$

Differentiate w.r.t. d

$$\frac{1}{60} = 0.016666666666666666$$

Steps Using Definition of a Derivative

Calculate 61 to the power of 2 and get 3721.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{d}{\sqrt{3721-11^{2}}})$$

Calculate 11 to the power of 2 and get 121.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{d}{\sqrt{3721-121}})$$

Subtract 121 from 3721 to get 3600.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{d}{\sqrt{3600}})$$

Calculate the square root of 3600 and get 60.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{d}{60})$$

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

$$\frac{1}{60}d^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{60}d^{0}$$

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

$$\frac{1}{60}\times 1$$

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

$$\frac{1}{60}$$