Solve 10^-10x/1.12*10^-12

$$\frac { 10 ^ { - 10 } x } { 1.12 \times 10 ^ { - 12 } }$$

Evaluate

$$\frac{625x}{7}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{10^{2}x}{1.12}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{100x}{1.12}$$

Divide 100x by 1.12 to get \frac{625}{7}x.

$$\frac{625}{7}x$$

Differentiate w.r.t. x

$$\frac{625}{7} = 89\frac{2}{7} = 89.28571428571429$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10^{2}x}{1.12})$$

Calculate 10 to the power of 2 and get 100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{100x}{1.12})$$

Divide 100x by 1.12 to get \frac{625}{7}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{625}{7}x)$$

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

$$\frac{625}{7}x^{1-1}$$

Subtract 1 from 1.

$$\frac{625}{7}x^{0}$$

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

$$\frac{625}{7}\times 1$$

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

$$\frac{625}{7}$$