Solve 2*22/7*0.7*h

$$2 \times \frac { 22 } { 7 } \times 0.7 \times h$$

Evaluate

$$\frac{22h}{5}$$

Solution Steps

Express 2\times \frac{22}{7} as a single fraction.

$$\frac{2\times 22}{7}\times 0.7h$$

Multiply 2 and 22 to get 44.

$$\frac{44}{7}\times 0.7h$$

Convert decimal number 0.7 to fraction \frac{7}{10}.

$$\frac{44}{7}\times \frac{7}{10}h$$

Multiply \frac{44}{7} times \frac{7}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{44\times 7}{7\times 10}h$$

Cancel out 7 in both numerator and denominator.

$$\frac{44}{10}h$$

Reduce the fraction \frac{44}{10} to lowest terms by extracting and canceling out 2.

$$\frac{22}{5}h$$

Differentiate w.r.t. h

$$4.4$$

Steps Using Definition of a Derivative

Express 2\times \frac{22}{7} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{2\times 22}{7}\times 0.7h)$$

Multiply 2 and 22 to get 44.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{44}{7}\times 0.7h)$$

Convert decimal number 0.7 to fraction \frac{7}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{44}{7}\times \frac{7}{10}h)$$

Multiply \frac{44}{7} times \frac{7}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{44\times 7}{7\times 10}h)$$

Cancel out 7 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{44}{10}h)$$

Reduce the fraction \frac{44}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{22}{5}h)$$

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

$$\frac{22}{5}h^{1-1}$$

Subtract 1 from 1.

$$\frac{22}{5}h^{0}$$

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

$$\frac{22}{5}\times 1$$

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

$$\frac{22}{5}$$