Solve 3b*10^10/56

$$\frac { 3 b \times 10 ^ { 10 } } { 56 }$$

Evaluate

$$\frac{3750000000b}{7}$$

Solution Steps

Calculate 10 to the power of 10 and get 10000000000.

$$\frac{3b\times 10000000000}{56}$$

Multiply 3 and 10000000000 to get 30000000000.

$$\frac{30000000000b}{56}$$

Divide 30000000000b by 56 to get \frac{3750000000}{7}b.

$$\frac{3750000000}{7}b$$

Differentiate w.r.t. b

$$\frac{3750000000}{7} = 535714285\frac{5}{7} = 535714285.71428573$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 10 and get 10000000000.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{3b\times 10000000000}{56})$$

Multiply 3 and 10000000000 to get 30000000000.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{30000000000b}{56})$$

Divide 30000000000b by 56 to get \frac{3750000000}{7}b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{3750000000}{7}b)$$

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

$$\frac{3750000000}{7}b^{1-1}$$

Subtract 1 from 1.

$$\frac{3750000000}{7}b^{0}$$

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

$$\frac{3750000000}{7}\times 1$$

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

$$\frac{3750000000}{7}$$