Solve 40/78*52/89x

$$\frac{ 40 }{ 78 } \times \frac{ 52 }{ 89 } x$$

Evaluate

$$\frac{80x}{267}$$

Solution Steps

Reduce the fraction \frac{40}{78} to lowest terms by extracting and canceling out 2.

$$\frac{20}{39}\times \frac{52}{89}x$$

Multiply \frac{20}{39} times \frac{52}{89} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20\times 52}{39\times 89}x$$

Do the multiplications in the fraction \frac{20\times 52}{39\times 89}.

$$\frac{1040}{3471}x$$

Reduce the fraction \frac{1040}{3471} to lowest terms by extracting and canceling out 13.

$$\frac{80}{267}x$$

Differentiate w.r.t. x

$$\frac{80}{267} = 0.299625468164794$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{40}{78} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20}{39}\times \frac{52}{89}x)$$

Multiply \frac{20}{39} times \frac{52}{89} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20\times 52}{39\times 89}x)$$

Do the multiplications in the fraction \frac{20\times 52}{39\times 89}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1040}{3471}x)$$

Reduce the fraction \frac{1040}{3471} to lowest terms by extracting and canceling out 13.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{80}{267}x)$$

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

$$\frac{80}{267}x^{1-1}$$

Subtract 1 from 1.

$$\frac{80}{267}x^{0}$$

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

$$\frac{80}{267}\times 1$$

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

$$\frac{80}{267}$$