Solve 2/5x*15/2

$$\frac { 2 } { 5 } x \times \frac { 15 } { 2 }$$

Evaluate

$$3x$$

Solution Steps

Multiply \frac{2}{5} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 15}{5\times 2}x$$

Cancel out 2 in both numerator and denominator.

$$\frac{15}{5}x$$

Divide 15 by 5 to get 3.

$$3x$$

Differentiate w.r.t. x

$$3$$

Steps Using Definition of a Derivative

Multiply \frac{2}{5} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\times 15}{5\times 2}x)$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15}{5}x)$$

Divide 15 by 5 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x)$$

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

$$3x^{1-1}$$

Subtract 1 from 1.

$$3x^{0}$$

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

$$3\times 1$$

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

$$3$$