Solve (3x)*(5x)

$$(3x) \times (5x)$$

Evaluate

$$15x^{2}$$

Solution Steps

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

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

Multiply 3 and 5 to get 15.

$$15x^{2}$$

Differentiate w.r.t. x

$$30x$$

Steps Using Definition of a Derivative

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

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

Multiply 3 and 5 to get 15.

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

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

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

Multiply 2 times 15.

$$30x^{2-1}$$

Subtract 1 from 2.

$$30x^{1}$$

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

$$30x$$