Solve 2x*65x^2

$$2x \times 65 { x }^{ 2 }$$

Evaluate

$$130x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$2x^{3}\times 65$$

Multiply 2 and 65 to get 130.

$$130x^{3}$$

Differentiate w.r.t. x

$$390x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}\times 65)$$

Multiply 2 and 65 to get 130.

$$\frac{\mathrm{d}}{\mathrm{d}x}(130x^{3})$$

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

$$3\times 130x^{3-1}$$

Multiply 3 times 130.

$$390x^{3-1}$$

Subtract 1 from 3.

$$390x^{2}$$