Solve (5.9*10^5)div(2*10^2)quadtext{(h)}(2.58*10^4)

$$( 5.9 \times 10 ^ { 5 } ) \div ( 2 \times 10 ^ { 2 } ) \quad \text { (h) } ( 2.58 \times 10 ^ { 4 } )$$

Evaluate

$$76110000h$$

Solution Steps

Cancel out 10^{2} in both numerator and denominator.

$$\frac{5.9\times 10^{3}}{2}h\times 2.58\times 10^{4}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{5.9\times 1000}{2}h\times 2.58\times 10^{4}$$

Multiply 5.9 and 1000 to get 5900.

$$\frac{5900}{2}h\times 2.58\times 10^{4}$$

Divide 5900 by 2 to get 2950.

$$2950h\times 2.58\times 10^{4}$$

Multiply 2950 and 2.58 to get 7611.

$$7611h\times 10^{4}$$

Calculate 10 to the power of 4 and get 10000.

$$7611h\times 10000$$

Multiply 7611 and 10000 to get 76110000.

$$76110000h$$

Differentiate w.r.t. h

$$76110000$$

Steps Using Definition of a Derivative

Cancel out 10^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{5.9\times 10^{3}}{2}h\times 2.58\times 10^{4})$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{5.9\times 1000}{2}h\times 2.58\times 10^{4})$$

Multiply 5.9 and 1000 to get 5900.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{5900}{2}h\times 2.58\times 10^{4})$$

Divide 5900 by 2 to get 2950.

$$\frac{\mathrm{d}}{\mathrm{d}h}(2950h\times 2.58\times 10^{4})$$

Multiply 2950 and 2.58 to get 7611.

$$\frac{\mathrm{d}}{\mathrm{d}h}(7611h\times 10^{4})$$

Calculate 10 to the power of 4 and get 10000.

$$\frac{\mathrm{d}}{\mathrm{d}h}(7611h\times 10000)$$

Multiply 7611 and 10000 to get 76110000.

$$\frac{\mathrm{d}}{\mathrm{d}h}(76110000h)$$

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

$$76110000h^{1-1}$$

Subtract 1 from 1.

$$76110000h^{0}$$

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

$$76110000\times 1$$

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

$$76110000$$