Solve =1.6*10^-21M

$$= 1.6 \times 10 ^ { - 21 } M$$

Evaluate

$$\frac{M}{625000000000000000000}$$

Solution Steps

Calculate 10 to the power of -21 and get \frac{1}{1000000000000000000000}.

$$1.6\times \frac{1}{1000000000000000000000}M$$

Multiply 1.6 and \frac{1}{1000000000000000000000} to get \frac{1}{625000000000000000000}.

$$\frac{1}{625000000000000000000}M$$

Differentiate w.r.t. M

$$0.0000000000000000000016$$

Steps Using Definition of a Derivative

Calculate 10 to the power of -21 and get \frac{1}{1000000000000000000000}.

$$\frac{\mathrm{d}}{\mathrm{d}M}(1.6\times \frac{1}{1000000000000000000000}M)$$

Multiply 1.6 and \frac{1}{1000000000000000000000} to get \frac{1}{625000000000000000000}.

$$\frac{\mathrm{d}}{\mathrm{d}M}(\frac{1}{625000000000000000000}M)$$

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

$$\frac{1}{625000000000000000000}M^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{625000000000000000000}M^{0}$$

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

$$\frac{1}{625000000000000000000}\times 1$$

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

$$\frac{1}{625000000000000000000}$$