Solve 5/2x5*x/25*x

$$\frac{ 5 }{ 2 } x \frac{ 5 \times x }{ 25 \times x }$$

Evaluate

$$\frac{x}{2}$$

Solution Steps

Cancel out 5x in both numerator and denominator.

$$\frac{5}{2}x\times \frac{1}{5}$$

Multiply \frac{5}{2} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 1}{2\times 5}x$$

Cancel out 5 in both numerator and denominator.

$$\frac{1}{2}x$$

Differentiate w.r.t. x

$$\frac{1}{2} = 0.5$$

Steps Using Definition of a Derivative

Cancel out 5x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{2}x\times \frac{1}{5})$$

Multiply \frac{5}{2} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 1}{2\times 5}x)$$

Cancel out 5 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x)$$

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

$$\frac{1}{2}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{2}x^{0}$$

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

$$\frac{1}{2}\times 1$$

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

$$\frac{1}{2}$$