Solve 4x/5*15x=

$$\frac { 4 x } { 5 } \times 15 x =$$

Evaluate

$$12x^{2}$$

Solution Steps

Cancel out 5, the greatest common factor in 15 and 5.

$$3\times 4xx$$

Multiply 3 and 4 to get 12.

$$12xx$$

Multiply x and x to get x^{2}.

$$12x^{2}$$

Differentiate w.r.t. x

$$24x$$

Steps Using Definition of a Derivative

Cancel out 5, the greatest common factor in 15 and 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3\times 4xx)$$

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3\times 4x^{2})$$

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{2})$$

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

$$2\times 12x^{2-1}$$

Multiply 2 times 12.

$$24x^{2-1}$$

Subtract 1 from 2.

$$24x^{1}$$

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

$$24x$$