Solve 16:2hdiv20:30

$$16 : 2 h \div 20 : 30$$

Evaluate

$$\frac{h}{75}$$

Solution Steps

Express \frac{\frac{\frac{16}{2}h}{20}}{30} as a single fraction.

$$\frac{\frac{16}{2}h}{20\times 30}$$

Divide 16 by 2 to get 8.

$$\frac{8h}{20\times 30}$$

Multiply 20 and 30 to get 600.

$$\frac{8h}{600}$$

Divide 8h by 600 to get \frac{1}{75}h.

$$\frac{1}{75}h$$

Differentiate w.r.t. h

$$\frac{1}{75} = 0.013333333333333334$$

Steps Using Definition of a Derivative

Express \frac{\frac{\frac{16}{2}h}{20}}{30} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{\frac{16}{2}h}{20\times 30})$$

Divide 16 by 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{8h}{20\times 30})$$

Multiply 20 and 30 to get 600.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{8h}{600})$$

Divide 8h by 600 to get \frac{1}{75}h.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{1}{75}h)$$

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

$$\frac{1}{75}h^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{75}h^{0}$$

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

$$\frac{1}{75}\times 1$$

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

$$\frac{1}{75}$$