Solve 3/2x*5x

$$\frac{ 3 }{ 2 } x \times 5x$$

Evaluate

$$\frac{15x^{2}}{2}$$

Solution Steps

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

$$\frac{3}{2}x^{2}\times 5$$

Express \frac{3}{2}\times 5 as a single fraction.

$$\frac{3\times 5}{2}x^{2}$$

Multiply 3 and 5 to get 15.

$$\frac{15}{2}x^{2}$$

Differentiate w.r.t. x

$$15x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{2}x^{2}\times 5)$$

Express \frac{3}{2}\times 5 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\times 5}{2}x^{2})$$

Multiply 3 and 5 to get 15.

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

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

$$2\times \frac{15}{2}x^{2-1}$$

Multiply 2 times \frac{15}{2}.

$$15x^{2-1}$$

Subtract 1 from 2.

$$15x^{1}$$

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

$$15x$$