Solve 30.36*22/68*h

$$\frac { 30.36 \times 22 } { 68 } \cdot h$$

Evaluate

$$\frac{8349h}{850}$$

Solution Steps

Multiply 30.36 and 22 to get 667.92.

$$\frac{667.92}{68}h$$

Expand \frac{667.92}{68} by multiplying both numerator and the denominator by 100.

$$\frac{66792}{6800}h$$

Reduce the fraction \frac{66792}{6800} to lowest terms by extracting and canceling out 8.

$$\frac{8349}{850}h$$

Differentiate w.r.t. h

$$\frac{8349}{850} = 9\frac{699}{850} = 9.82235294117647$$

Steps Using Definition of a Derivative

Multiply 30.36 and 22 to get 667.92.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{667.92}{68}h)$$

Expand \frac{667.92}{68} by multiplying both numerator and the denominator by 100.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{66792}{6800}h)$$

Reduce the fraction \frac{66792}{6800} to lowest terms by extracting and canceling out 8.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{8349}{850}h)$$

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

$$\frac{8349}{850}h^{1-1}$$

Subtract 1 from 1.

$$\frac{8349}{850}h^{0}$$

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

$$\frac{8349}{850}\times 1$$

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

$$\frac{8349}{850}$$