Solve 1.6/281.15x*1.045/308.15

$$\frac{ 1.6 }{ 281.15 } \frac{ x \times 1.045 }{ 308.15 }$$

Evaluate

$$\frac{3344x}{173272745}$$

Solution Steps

Expand \frac{1.6}{281.15} by multiplying both numerator and the denominator by 100.

$$\frac{160}{28115}\times \frac{x\times 1.045}{308.15}$$

Reduce the fraction \frac{160}{28115} to lowest terms by extracting and canceling out 5.

$$\frac{32}{5623}\times \frac{x\times 1.045}{308.15}$$

Divide x\times 1.045 by 308.15 to get x\times \frac{209}{61630}.

$$\frac{32}{5623}x\times \frac{209}{61630}$$

Multiply \frac{32}{5623} times \frac{209}{61630} by multiplying numerator times numerator and denominator times denominator.

$$\frac{32\times 209}{5623\times 61630}x$$

Do the multiplications in the fraction \frac{32\times 209}{5623\times 61630}.

$$\frac{6688}{346545490}x$$

Reduce the fraction \frac{6688}{346545490} to lowest terms by extracting and canceling out 2.

$$\frac{3344}{173272745}x$$

Differentiate w.r.t. x

$$\frac{3344}{173272745} = 1.9299053639393777 \times 10^{-5}$$

Steps Using Definition of a Derivative

Expand \frac{1.6}{281.15} by multiplying both numerator and the denominator by 100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{160}{28115}\times \frac{x\times 1.045}{308.15})$$

Reduce the fraction \frac{160}{28115} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{32}{5623}\times \frac{x\times 1.045}{308.15})$$

Divide x\times 1.045 by 308.15 to get x\times \frac{209}{61630}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{32}{5623}x\times \frac{209}{61630})$$

Multiply \frac{32}{5623} times \frac{209}{61630} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{32\times 209}{5623\times 61630}x)$$

Do the multiplications in the fraction \frac{32\times 209}{5623\times 61630}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6688}{346545490}x)$$

Reduce the fraction \frac{6688}{346545490} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3344}{173272745}x)$$

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

$$\frac{3344}{173272745}x^{1-1}$$

Subtract 1 from 1.

$$\frac{3344}{173272745}x^{0}$$

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

$$\frac{3344}{173272745}\times 1$$

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

$$\frac{3344}{173272745}$$